Designing and Optimising of a Dynamic Vibration Absorber Assignment

1. Introduction Designing And Optimizing Of A Dynamic Vibration Absorber For A Continuous Mechanical Structure To Attenuate Mechanical Vibration

Feeling overwhelmed with your assignments? Take a breather and let New Assignment Help ease your burden! Our professional team provides unmatched assignment writing services in the UK, guaranteeing academic success. Explore our free Sample for students for inspiration and guidance.

The aim of this assignment help Uk work is to design and optimise a dynamic vibration absorber which can be used to reduce the mechanical vibration in mechanical structures on which they are installed. Dynamic Vibration Absorbers (DVAs) are passive equipment mounted in mechanical systems to reduce the vibration of the mechanical structure at certain frequencies. A mass – damper – spring system is used as the basic motion damping block in a mechanical system (Broch, 1984). The initial damping systems developed never had a damping element, but instead had a secondary mass element which was attached to the principal mass using a secondary spring (Broch, 1984). This absorber was effective in a constrained range of frequencies which are closer to the natural frequency of the principal system (Broch, 1984). This type of system is capable of reducing vibrations having frequencies which are closer to the natural frequency range of the main system to which the absorber is attached (Broch, 1984). But when resonant frequency vibrations occur such systems are not capable of attenuating such frequencies and this type of system is called tuned mass damper system. This work is aimed at developing a dynamic vibration absorber for reducing mechanical vibrations.

The term “Dynamic Vibration Absorber” is also known by the names “Tuned Mass Dampers”, and “Vibration Neutralizers” in general. This is a mechanical appendage which consists of inertia, damping elements, and stiffeners that are attached to the machine in question to absorb the energy of vibration at the point of connection. This helps the system in focus to stay protected from the extremely high degree of vibrations. In reality, the “DVA” can very well be incorporated into the design pertaining to the original system or the existing system by way of a remedial mode of action. Nowadays, the dynamic vibration absorbers are used extensively for the purpose of bringing down the vibration levels in different categories of mechanical systems. In case of the practical; applications, the dynamic vibration absorbers could be witnessed in different configurations which are intended to reduce the angular or rectilinear motion for that matter.

1.1. Project Aim

The sole aim of this particular project is to construct and develop a “Dynamic Vibration Absorber” to reduce the mechanical vibrations in case of a continuous structure by way of “Finite Element Analysis” in “Matlab”, and “Ansys”.

1.2. Project Objectives

• To create a suitable model of “DVA” within “Matlab”, and “Ansys” Design Modeler
• To thoroughly evaluate the performance level regarding the “DVA” with the help of “Finite Element Analysis” inside Ansys
• To bring about a “three-dimensional” coupled dynamic in respect of vibrational isolation by way of the “parametric” design language called Ansys
• To determine the “vibration isolation” performance pertaining to the “DVA” provided that the harmonic and dynamic conditions of loading are in effect

1.3. Background

The dynamic vibration absorbers are essentially attached to the host structure for controlling the motion. These types of devices are used rapidly for controlling the vibration ensuing from the aircraft frameworks (Roozen et al. 2021). The operation of this type of device depends on the manner in which their application takes place. One of the ways to operate this type of device is to suppress the underlying vibration at a specific “forcing frequency”. In such cases the natural frequency of the device gets tuned to the excitation frequency. The damping factor pertaining to the concerning device is to be low in particular, for rendering the most amount of resistance to the underlying framework at the “operating frequency”.

This particular device gets known by the name of “vibration neutralizer” in general. Moreover, this device can also be used for mitigating the vibration produced from a specific mode of structure across a set of frequencies. In this case, the device gets known as “Dynamic Vibration Absorber”. The ratio of damping along with the optimum tuning regarding the natural frequency of the concerning device becomes less prominent. It is also predicted on the manner in which the criteria optimization gets defined.

1.4. Scope of the Research

In the case of aircrafts, it is extremely crucial to ensure the stability of the aircraft so that the degree of comfort and convenience remains top-notch. This would not only render a hospitable environment for the crews but for the passengers as well. In the context of this research, it is very obvious to consider the dynamic vibration absorbers by way of the way they are incorporated in the aircraft's frame (Yang et al. 2022). The usage of these damping absorbers is rising day by day as far as the place of application is concerned. In the aerospace industry, any slight deviation from the ideal condition of the aircraft parameters can bring harmful outcomes. Vibration, which if goes above a limited range can tamper with the aircraft's performance, resulting in the degradation of passenger experience. So, it can very well be predicted based on the present scenario that the application of such absorbers will not only go up in quantity but also in clarity too for that matter.

1.5. Themes

Damping vibration absorber essentially eliminates all of the unwanted vibrations that are produced inside of any system. It comprises an auxiliary system along with an attached “absorber mass” which constitutes a system having “2 degrees of freedom”. It is obvious for this type of system to have two types of natural frequencies based upon its objective of application. The spring mass “DVA '' in this case operates across a range of narrow frequencies and also suffers from deterioration in performance owing to the change in excitation frequency (Yoon et al. 2021). The introduction of the factor of damping helps to enhance the robustness of performance. In comparison to the un-damped “DVA”, damped “DVA” has got lower response along with increased range of operational frequency.

1.6. Dissertation Plan

This particular Dissertation is structured in the following manner:

Chapter 1: This chapter deals with the introduction part which illustrates the very concept and workings of the Dynamic Vibration Absorber. The aims as well as objectives are also explained along with the aforementioned part.

Chapter 2: In this chapter the focus is on the Literature review. This chapter thoroughly analyzes the previously performed works, existing gaps in the literature, along with elaborating on the crux of the issue.

Chapter 3: This chapter is known by the name Methodology, which lists out all of the techniques and approaches that are abode by to bring a solution to the issue in question.

Chapter 4: This particular chapter deals with the aspect of simulation inside the platform of Matlab. The results obtained from creating a “Mass” spring damper having a 3-degree or 2-degree freedom is also discussed.

Chapter 5: In this chapter, the simulation aspect inside the Ansys platform is taken into consideration. All of the related results are also discussed in relation to an “un-damped” system having “2-degree” freedom.

Chapter 6: This section explains in brief regarding all that have been performed in this research project in general.

Chapter 7: This chapter consists of a set of recommendations that are useful in the case of further developing this project in the long run.

The Appendices along with the Gantt chart are also included at the end of the final chapter in order to execute the project timeline as well as project schematic respectively.

2. Literature Review

The performance of mechanical systems is affected negatively by vibrations which might lead to equipment damage, energy loss, and mechanical parts erosion and so on. Composite materials have been used extensively in various applications of research and engineering especially in the recent development within the aerospace industry, submarine and automotive structures. This is due to the high strength to stiffness ratio and light weight structure they have when compared to other metallic materials. These highlight their merits along with their potential to be customised and tailor designed for achieving specific design parameters with lower weight and increased strength. Composite vibration analysis is a major challenge in composite structural design.

The vibration absorber mechanism of any mechanical structure is the base support that protects the total mechanical structure from any sort of accident. Without proper support from the vibration absorber, big mechanical structures like bridges, vehicles, and aircraft are unable to avoid great disasters and accidents. The research in the field of improving new models of vibration absorbers is still going on and many innovative designs are coming into the market. The vibrations absorbers is supporting all the mechanical structures in as many ways as possible. For big structures like in the case of bridges, the “Stock bridge damper” is used as a vibration absorber which is a “TMD (Tuned Mass Damper)”.

This absorbing mechanism for the bridges can suppress the induced wind vibration on the slender structures of the bridge like the power cables of the bridges, “long cantilevered signs” and “the cable-stayed bridges”. The vibration absorption system for the vehicles is the main suspension mechanism of the vehicle with the “torsional vibration damper” also used for absorbing all the rotational vibrations for the “IC engines”. In the case of the aircraft, the vibration absorption is done by the “turbofan operator” and with the help of simple maintenance by the “turbofan operator,” the engine vibration of the airplane can be kept under control. The topic is mainly about the design and makes optimization of the “Dynamic vibration absorber” which is also known by the name of “Tuned mass Dampers”.

2.1. Background

The concept of the “Dynamic vibration absorber” is first applied by “Frahm” in the year of 1909. By using this concept the rolling motion of the ships along with the ship hull vibrations. A research paper on the topic of TMD was published later in the year of 1928 by “Ormondroyd and Den Hartog”. After this research, the next paper includes a detailed discussion on the topic of “optimal tuning” and parameters related to the damping vibrations published in the year 1940 by “Den Hartog”.

The earlier research on this topic is about “Frahm's undamped SDOF system” which is caused by the force of sinusoidal excitation. Another researcher name “Brook” in the year of 1946 took a different path in research which is a more efficient method for improving the field of developing dynamic vibration absorbers. The method does not consist of differentiation methods and from the research results the ratio of the optimum damping model is implemented in this research. Another researcher named “Srinivasan” researched this optimized parameter of the damping ratio for designing a parallel damped “dynamic vibration absorber or (DVA)” in the year of 1969.

Figure 1: Damped Dynamic Vibration Absorber Model

Another research paper which is published in the year of 2004 by “Kefu liu and Jieliu” provides a model of the optimized parameters ratio of the “damped dynamic vibration absorbers”. Another part of this research is about the “SDOF systems” and this research on these “SDOF systems” is conducted by many researchers. By using the external power supply the “active control devices” can operate easily so these “active control operators” are much more efficient than the “passive control devices”. However, problems arise when “control-force capacity” becomes insufficient and a huge power supply is required in the current technology of the structural control for countering against the high scale earthquakes. These problems are the major issues in the modern technology of the “DVA” that needs to be overcome. To solve this problem a technical solution is available in the market which can use both active and passive control devices.

The name of this new control device is “semi-active control device” and it is very attractive in the market because of its very low power consumption and proper stability. The previous research papers are about the topic of “SATMD” and this research is done in the year 1983. The researcher presents the “SATMD”, and “TMD” which is controllable damping that includes time variation.

In the case of identical conditions, the behavior of the “SATMD” instead of the “TMD” is more efficient considering the structural control.

2.2. Description and comparison of the approaches undertaken

The definition of the “DVA or dynamic vibration absorber” can be explained as the “DVA” is the conjunction of a “tuned-spring mass system”. Using this system the vibration or the shockwaves of a mechanical structure can be eliminated or reduced. The invention of the “DVA” is done by the researcher” Hermann Frahm” in the year of 1909 after that, the “DVA” was used to suppress the vibrations induced by the wind and reduce the “seismic response” for buildings. The “SATMD” control design system is not suitable for the parameters like mass, ratio, and frequency. The structure with TMD is tuned for first-mode response in the fundamental frequency of the mechanical structure.

For overcoming the problems related to the frequency in the case of using one “TMD” so more than one “TMD” is installed in the mechanical structure. The frequency of every “TMD” is tuned according to the mechanical structure requirement. The researcher name “the clerk” proposed the report about the concept of the “Multiple Tuned Mass Dampers (MTMDs)” and its optimization process. There is some research conducted by researchers about the usage of the “MTMD” along with the “doubly tuned mass damper (DTMD)”. In the case of the” harmonic excitation” and “zero-mean white-noise random excitation” the total efficiency of the “DTMD” is in the case of supporting the mechanical structure and reducing the vibration of the structure.

The research analysis shows the difference between the usages of the “DTMD” over a single mass ratio method “TMD”. The usage of the “DTMD” is more conventional than the “TMD” for all the range of the mass ratios. The recent research on the numerical and experimental analysis of the “TMD” is carried out for detecting the total efficiency of reducing the vibrations of the structure in the seismic response. In the year 1994, the three different models for analyzing the impact of the vibration on the mechanical structures are represented. The first is a 2D model which is about the shear building of two-story.

Next is a 3D model for the frame building of one story and the third model is also a 3d model of the bridge which is cable-stayed. This structural analysis is created using a total of 9 different earthquake records. The numerical analysis explains the response time of the “TMD” in different earthquakes for different structures is not the same for the same types of earthquakes. Some of the structure “TMD” responses were very efficient and but some structures are affected by the earthquakes so the “TMD” response is not effective. This analysis shows that different “TMD” in different structures' response times for reducing the vibration depends upon certain characteristics of the earthquake and the ground motion (Abdullah et al. 2021).

The response for reducing the vibration of the structure is huge in the case of resonant ground motions and diminishes when the main dominant frequency of the vibration goes further away from the mechanical structure. The effectiveness of the “TMD” is very limited for vibration-like seismic loading so to solve this problem the “MTMD” is installed in the structural construction for reducing the impact of the vibration. In the year of 1988, a new research paper is published related to the “multiple-tuned mass damper” which is able to reduce the impact of vibration on the building and mechanical structures.

This research methodology is based on the work of the researcher name “Den Hartog” and the research topic is based on the “single degree of freedom” and “multiple degrees of freedom”. In the year 1940, the simplified version of the “linear mathematical” models is represented by the statistical analysis of the “El Centro earthquake” and the response of the “TMD” is very useful for reducing the vibration of the earthquake and saving the building and the structures. Using parametric studies the development of increasing the performance of the tuned mass dampers under the induced wind condition and the performance of the both “passive and active tuned mass damper” can be done. From the few experimental and numerical analyses it can be stated that the “TMD” theory mainly consists of active control research and but using the parametric study the results of this experiment can be compared very well (Dai et al. 2021). The “TMD” has several constraints in the design but the usage of the “passive and active tuned mass damper” systems is necessary. So these two systems are installed in tall buildings and mechanical structures for reducing the dynamic impact of the induced wind and earthquakes.

In 1996 a research paper proposes the “passive vibration absorber” which is able to support tall and high-rise buildings and structural systems against the damages done by the earthquake. A new structure of “TDM” is prosed for the “one-mass” system and a “cantilever” system. The damping of the mechanical structure and vibration absorber is installed on the top of the structure. A new ground movement is designed by the actuator which is able to produce the vibration with different amplitude and frequencies. In 1996 another research paper is published about the implementation and usage of mass damper systems (Luo et al. 2019).

The mass damper system usage and its effects are clarified which is mainly about the many recorded values of the actual building against the induced wind vibrations and earthquakes. The discussion of this effect is based on the natural time period of buildings that are equipped with “mass damper systems”, “mass weight ratios to building weight”, and the “wind force levels” along with earthquake and the levels of ground motion. In 1997 a new method for the take an estimation of the parameters of tuned mass dampers in the case of seismic applications is developed.

In this research optimum parameters of the usage of the “TMD” in the building for reducing the impact of the vibration in the response of the mechanical structures to seismic loading of the design are mentioned in this research. The criterion that is taken into consideration for obtaining the optimum parameters is the mass ratio of the “TMD”, the frequency of the vibration, and damping ratios. These optimum parameters are used for calculating the several “single and multi-degree of freedom” of the big mechanical structures with installed “TMD” in different earthquake conditions. The results of the experiment show a significant reduction in the displacement and acceleration of the “TMD”s which are installed in the structures. Using this method of vibration control for mechanical sub-structures and configurations where these structures are used as vibration absorbers can be done. In the 1996 paper published about the “concise point of departure” for researchers who are wise to improve the current state and the design of the “DVA” and monitoring different structures made by civil engineers.

This theory helps to make links between structural control and many other fields like active and passive control of the structures and points out the similarities and dissimilarities along with its future research and application. In the year 2001, a research paper is published about the “Optimal placement of multiple tuned mass dampers” in the case of seismic structures. In this research, all the effects of the “tuned mass damper” and the modal responses against the earthquake for the Six-story building structure are studied and analyzed (Lang et al. 2020). The new form of tuned mass dampers like the multistage and multimode model is developed to make advances toward evolving the “DVA”. In this project design for the “DVA” is done using the software called “Ansys”. The effectiveness of the “TMD” is necessary for supporting the structures of the building (Bahrami et al. 2019).

The importance of the vibration absorber totally depends upon the mass ratio of the “TMD” and the frequency of the vibration. The design of the “DVA” must need to clarify that the structural failure because of the induced wind and the earthquake is inducing damage to the structure. In the year 2003 a research paper in publishes about the performance of the “DVA” in a five-story building and the benchmark model for the usage of the “active tuned mass damper” and a “fuzzy controller”. The research paper is about measuring the performance and efficiency of the “five-story benchmark model” by using the “active tuned mass damper (ATMD)” and the control over this action is achieved with the help of “Fuzzy logic controller (FLC)”.

The main advantages of the “Fuzzy controller” are the inherent “robustness” and the ability to handle all non-linear structural failure behavior. The usage of the “TMD” and both the active and passive control in structural failures is necessary. In 2004 another research paper is published explaining the induced Wind Response Control over the many mechanical structures with the help of Variable Stiffness in the “TMD”. In the year of 2006, an advanced research paper is published about the optimal analysis theory of the application of the usage of the TMD. In 2007, another research paper is published for supporting the “Optimum design and the structural analysis for the “passive tuned mass dampers” which are used in viscoelastic materials. In 2008 a research paper is published about the “Seismic Energy Dissipation of Inelastic Structures” with help of the “TMD” is discussed. To support this research another research paper is published about the “Dynamic analysis” of mechanical structures using the “multiple tuned mass dampers (MTD)”.

In the year of 2009 new research is developed for determining the efficiency and performance of a “nonlinear tuned mass damper (TMD)”. The latest research in the year 2010 is published on the topic of Vibration control for different seismic structures with the help of semi-active friction “multiple-tuned mass dampers (MTMD)”. This paper is about making a comparison of the system which uses the “passive friction-type multiple tuned mass dampers (PF-MTMDs)” and this ability to demonstrate the efficiency and the effectiveness of the “SAF-MTMD” which is able to suppress the seismic motion of a big mechanical structural system, and the visible to reduce the reducing the strokes of each and one mass unit, especially for high-scale earthquakes.

The methods discussed are the latest research related to developing the “dynamic vibration system’ for mechanical structures like bridges and aircftats, etc. the effectiveness and the efficiency and the performance of the “DVA”. This report is about discussing the new methods for the designing and optimizing the in the “Ansys” software. Using latest methods and technology the development of the “DVA” preceding rapidly to support the field of mechanical engineering.

2.3. Summary of research gaps in the existing work

Here, almost all of the research papers have considered the very basic design of the “DVA” in the form of a system pertaining to a spring mass (ASAMI et al. 2021). The reason for the aforementioned fact is the existence of a very simple framework which can verily be implemented without much expense. In this case, the suppression performance is limited to a certain extent which creates resonant frequencies that are to be averted. In most of the instances, the focus stayed on either “one” or “two” degrees of freedom in general while constructing the “DVA”. The drawback in this regard is the absence of proper study regarding the entire performance of “DVA” in respect of many degrees of freedom. The theoretical calculations have been done by way of the “un-damped” theory. But, these essentially require the presence of the factor of optimization in terms of the real world situations for being implemented in the definite use case in particular.

In the case of deducing a large set of vibration frequencies the development of numerous degrees of freedom “DVA” has to be in effect (Feudo et al. 2019). This in turn pertains to the enhancement of the total number of components present in the absorber along with its entire weight. The development of certain materials that have the capacity to absorb the vibrations over a range of frequencies can bring about a solution to the aforementioned issue. In the present situation, the polymer called “Sorbothane” is generally considered to act in the form of a best possible vibration absorber in respect of the issue in question.

A large quantity of the mass “spring damper” systems incorporate the material called stainless steel for the purpose of designing a vibration absorber. The point of concern here is that the aforementioned material is quite heavy as compared to the material aluminum. When it comes to the aircrafts, the width as well as the weight of stainless steel is to be brought down for optimal performance. Otherwise, it has the potential to enhance the factor known as “bucking”. Whereas, aluminum is lighter in weight as opposed to steel along with having an excellent capacity to absorb energy. This in turn refers to the aforementioned material to be the ideal one to absorb vibration. It also has the potential to bring down the “bucking” factor by dint of an increment in the material’s thickness.

The orientation of any absorber plays an important part in reducing the generated vibration. The absorber does not work efficiently when placed near the node of vibration in respect of the system in question (Ha et al. 2021). When it comes to the development of vibration absorbers for sophisticated systems, a set of suitable formulations are verily needed as far as the system is concerned. This in turn helps in evaluating the physical attributes of that vibration absorber.

2.4. Problem Definition

Fundamentally, the dynamic vibration absorber refers to a particular tool that helps to attenuate the generated noise as well as the structural vibrations. The underlying efficacy is contingent upon the reduction of structural vibrations at the narrow “band” level in particular. This also assists in bringing down the heavy vibrations along with greater levels of stability. The aforementioned factors are termed as being one of the primary reasons to incorporate vibration absorbers in the cabin of the airplane (Hua et al. 2018). VBA is essentially situated in relation to the target for that matter. The underlying working principles pertain to the reverberation produced by the main system, which in turn facilitates the absorber’s vibration. The ensued movement from the “DVA” produces the force of reaction which then gets disseminated to the main system. This thoroughly helps to control the main system’s vibration to a certain degree (Infante et al. 2018). In this case, the incorporation of supplementary “DVA” within the system in the form of a subsystem helps to boost the capacity of vibration control to a greater degree.

The inclusion of “DVA” in the cabin of the airplane mitigates the impact of noise ensued from the engine of the aircraft right up to the cabin area. This result is obtained with the help of low frequency and light weight “DVA”. In the case of the aircrafts there exists two categories of vibrations in general. One of these is the low frequency vibrations which are less than “20 Hz”. This kind of vibrations can be experienced by the whole of the body. The source of these vibrations is the existence of heavy components in the airplane, such as the horizontal stabilizer, elevator, and rudder, which are attached to the airplane’s frame. Another is the high frequency one, having a frequency greater than “25 Hz”. The hands and feet of the human body can experience the aforementioned frequency type. This vibration type comes from the small components present in the airplane, such as the door that is fixed on the aircraft’s frame. As the velocity of the airplane fluctuates and so do these vibrations.

The fundamental framework of the “DVA” consists of a number of components, such as quality, damping as well as stiffness. This absorber works as a subsystem attached to the vibration damper in the form of a target (Ji et al. 2022). Here, the ensued force of reaction brings down the level of vibration by way of resonance factor. An ideal vibration absorber is slated to contain a high “damping ratio” so as to suitably mitigate the vibrations.

On the basis of literature review a passive “DVA” equipped with a “mass spring damper” system is constructed for the purpose of fulfilling the desired objective. The aspects such as the design as well as analysis are predicted on the platforms of software called “Ansys”, and “Matlab” respectively. Here, “Aluminum Alloy 6061” is chosen to build the aforementioned system. This particular material has “2700 kg/m³ density, “310 MPa” tensile strength, and “250 MPa” tensile yield respectively. All of these attributes make this material suitable for any number of applications within the industry of aerospace. Here, Transient Analysis, Modal analysis, and statistical analysis have been taken into account for explaining the fundamental issue. Moreover, the simulation analysis is performed so as to validate the vibrations absorbers’ performance.

2.5 Data Analysis

Data analysis is crucial for c carrying out the implementation process in Ansys software. The software analysis has to be carried out for having the practical demonstration. The buildings or structure has to be designed in such a way that there could be minimum damage. The structure has to be analyzed in Ansys software so that all the insights could be understood to avoid any further structural damage. The structural damages could be avoided only if the reasons could be understood by the user. Ansys software has all the settings as well as features that could be further used for 3d modeling design as well as all the calculations. The calculation part has to be investigated to make sure there could be some prevention techniques. The prevention techniques could be used for preventing any structural failure. The interface has all the data that has to be provided one after the other for carrying out practical demonstrations. The instructions need to be carefully demonstrated for having a model design (Lang et al. 2020).

Basically, Ansys helps in carrying out FEA analysis. FEA analysis could be helpful in providing an accurate design. Many important issues like heat transfer, buckling analysis, and also thermal analysis. The objective is to design such a model that could prevent the damage caused by vibration. Any particular structure has to go through various types of loads. Earthquakes for decades have started causing damage to structures. The structures consist of parts that have to be designed so that any damage could be prevented. The structures like buildings, bridges and many more are designed by having reinforcement in it. Mechanical structures usually consist of concrete mix, as well as steel bars so that the building could be rigid as well as strong enough. Ansys software is there to help out civil engineers by carrying out FEA analysis.

3. METHODOLOGY

3.1. Introduction

The proper and accurate process is the main key to achieving success for any project and also for the organizations. Here in this project have to design and also optimizing a dynamic vibration absorber for a continuous mechanical design to reduce mechanical vibration. Here a structure is very important to construct a thing mechanically or physically and a mechanical structure which is everywhere and implemented in everything (ASAMI et al. 2021). Here the vibration excitations in mechanical structures like buildings, bridges, pipelines, and many others are produced by the natural cause and also for some human activity basically by the heavy machines used in the construction process. If the vibrational frequency is similar to the natural frequency then there occurs many problems and damages which was faced by the mechanical structures and the construction company and the projects are leads to failure. Here the dynamic vibration absorber absorbs the produced vibration and reduced the vibration frequency in the mechanical structure and decreased the damage rate of the constructal structure. Basically, the vibration absorber is used in the pipeline system project because the pipeline of a mechanical structure faces most of the vibration which is created by the turbulence of the water flow. The vibration absorber basically consists of a mass and an adjustable segment to decrease the vibration rate in the mechanical structures.

A dynamic vibration absorber basically disperses the produced vibration or energy and one of the most important things is for the vibration absorber to use or normalize the absorbed energy into the heat which stays in the viscous fluid. There are other ways to dissipate energy, for electromagnetic the absorbed vibration, can be stored in the form of heat and used later.

3.2. Research Approach

Essentially, the research approach is of three types which are known as Deductive approach for research, Abductive research approach, and Inductive approach of research. The deductive approach is contingent on the fact of developing a particular hypothesis or a set of hypotheses that are predicted on an existing theory. In this approach, the factor of reasoning moves from particular to general on the whole (Luo et al. 2019). The abductive research approach aims to address all the weaknesses linked with the rest of the research approaches. In this kind of approach, the process of the research begins with “puzzles”, or “surprising facts”. The aforementioned factors emerge at that time when the concerned researchers come across an “empirical” phenomenon which cannot be elucidated with the help of the existing theories.

In the case of the inductive approach of research, the process begins with the theories as well as the observations which are brought about at the end of the “research process”. This approach aims for the abstraction of patterns from the observations. The development of the explanations and theories takes place in respect of these patterns with the help of a set of hypotheses in general. In the present context of the research, the Deductive Approach has been taken into consideration.

3.3. Research Design

The term research design pertains to the basic framework of the research methods as well as the techniques selected by the concerned researchers in order to conduct the whole of the study. It permits the researcher to suitably sharpen all of the research methods suitable for the core of the research topic. The type of research design is very crucial with respect to the aspect of selecting the best model for the study in question. The design of research has been classified in two sections, which are Qualitative design of research, and Quantitative design of research respectively.

Quantitative Design

This kind of research design helps to determine the underlying relationship amongst the gathered data along with the observations predicated on the mathematical calculations (Noori et al. 2019). The statistical methods can easily disprove or prove the theories linked to any natural occurring phenomenon. It also assists in determining “why” any specific theory is in existence along with “what” all the respondents have to conclude about it.

In this specific research, the Qualitative Design has been considered to perform the corresponding tasks.

Qualitative Design

This type of research design is applicable for such cases wherein the statistical conclusions for collecting the “actionable insights” are crucial. Here, the numbers render a better perspective in order to make critical “business decisions”.

3.4. Develop a dynamic vibration absorber in ANSYS and perform Statistical Energy Analysis (SEA)

An impenetrable system of acoustic and structure most likely to be sketched as a mixture of N subsystems relies on conditions of their connections. The coupling loss factor and energy loss are the key features that determine the energy transmissions among the subsystems. In this case, subsystem the energy equations of can be written as represented by equation Error: Reference source not found)

(1)

Where,

P - Input power, – Energy loss factor, w – Coupling loss factor

The aircraft composite panel that we have considered here is a double-wall like structure and it is subdivided into five different substructures as shown in Figure 2.

Figure 2: Substructures Block-diagram of aircraft Composite Panels

The energy equation defining the impound surveillance to airborne excitation can be represented by equation Error: Reference source not found),

= (2)

We are able to estimate the transmission loss by equation Error: Reference source not found),

(3)

Where, S is the panel Area

3.5. Determination of SEA Parameters by indirect Coupling Method

The evaluation of SEA parameters can be done using different approaches but the most suitable approach for weak coupled structures is the loss factor of indirect coupling theory of traditional SEA as it would result in more efficient results.

The indirect coupling factors can be derived from equations (Error: Reference source not found) and Error: Reference source not found) for N number of substructures that are coupled in series array,

(4)

(5)

These equations indicate that if the coupling of the substructures is weak, there might be negligible loss factor whereas for a strong coupling it would be of significant indirect coupling.

3.6. Simulation Setup in ANSYS

The composite panel from an actual aircraft composite panel of dimension 1.42mx1.58 m and 0.8 mm thick is shown in Figure 3. The double wall structure was constructed using a 0.4mm thick aluminium panel. The testing panel is installed between a vibration area and a non-resonant bower as shown in Figure 3. The vibration area was of volumetric dimensions of 5.60m x 4.30m x 3.75m and that of non-resonant bower of 4.40m x 4.60m x 3.10m. Sources for generating vibrations were placed in the vibration area and the non-resonant bower in the receiving space.

Figure 3

1. c The Composite panel. 3. c Installation of panel3. c Stringer cross-section

The procedure for loss of transmission test is archetypal. The natural frequencies and vibration modes were obtained by the modal analysis test and results would be tabulated. These tested data would eventually be used for the comparative evaluation. Figure 4 shows the designed dynamic vibration absorbers which are viable to be tuned at the desired frequency. The fuselage is riveted with the absorber parallel to the panel. The mass spring damper system as shown in Figure 4 is simulated in ANSYS with two degrees of freedom.

3.7. Experimental setup and design

Here in the process of making a dynamic vibration absorber, an experiment is very necessary for the mechanical structure. Basically, an experimental model has four parts which are the mechanical structure, unbalanced weighted motor, vibrometer, and beam DVA. Here produce a practical arrangement of the mechanical structure which is similar to the actual project or the constructional structure to test the vibration absorber functionality. Here the geometric and physical properties of the mechanical structure are used in the experimental model to execute the theoretical and the practical test for the structural safety concern. Therefore the unbalanced weighted motor is used in the mechanical structure to produce the excitations. This motor is connected to a frequency drive where it can give the desired frequency for the mechanical structures. It can be increasing and also decrease as per the testing requirements where the absorber can test it practically. Next, the vibrometer is here in the absorber monitoring the frequency which has a specific range between 2 to 10000Hz and it is also able to measure the acceleration, velocity, and displacement in the mechanical structure. In the end, the beam DVA is a model which contains an L-shaped beam to absorb the kinetic energy both horizontally and vertically. It is mostly used in beam construction projects where threaded rods are used to construct the beam (Love et al. 2021).

This beam structure experimental setup is basically an effective test bed for the vibration absorber and it is also used in many engineering fields.

The following research is the basis of a vibration-absorbing system dynamically. The resources to collect the datasets from various resources like journals and articles can be observed to further utilize the concept (Lang et al. 2022). This is a mechanical implementation on the bases of several application-based vehicles or large kinds of buildings for the purpose of absorbing vibration. There are many purposes of the vibration that can occur on the bases of different scenarios, so every perspective of the bases of vibration occurring has to be observed. There are many such vibration isolation techniques that have to be observed and it can be stated in different dimensional stages so every aspect has to learn the perspective. There the purposes of preventing vibrational isolation, the parametric design to the reflective optimization, “Ansys '' are generated three-dimensional model based designing for the purpose of finite kind of element base analysis. There are several design modelers that can be used to design their purpose in terms of vibrational isolation (Venczel et al. 2020). The purpose of controlling motion in the structure-based mechanism and the application based on the different frequencies of the framework to neutralize the vibration is to observe by collecting the database to find the total phenomena of the modelling.

The represented analytics purposes various experimental designing can be taken to observe the different perspectives (ZHANG et al. 2021). There are several geometrical approaches that can be taken to implement the configured model, the geometrical approaches can be specified in the bases of the piston, spring, or the other connective property, and the structural materials are figurized in the coordinate-wise functionality, and the many several contracts regions to resist the vibrational effect, the purpose of the said functionality bases the actual modelling can be done in design analytic languages. There are several thermal conduciveness can be observed graphically in the purpose of pressure (Zhou & Hou, 2020). The structural methodology can be specified in many aspects like the isotropic elasticity of the structural steel in various ratios or modulus beneficiary, it can be derived from “Bulk Modules” or the basses of “Poisson’s Ratio”, the comprehensive straightness of the structural methodology can be observed in much geometrical structure. The analysis can be processed in various harmonic response analyses, for the purpose of rotating the speed in three purposes of frequency. The effectiveness of several heat-transmitting properties, the particular representation is basically done to the simulation purposes in the system without any presence of vibrational isolation.

The finite element-based structural model is testing the natural frequency in terms of various curve filtering to transfer the structural execution in a decorated way. There is various kind of module-based operators to figure out the row and column-based executing properties. The finite-based element methods are implemented in various dipole-based modification, dipole is basically structured in silicon kind of steel-based modification to compose the mechanism functionalities. The many natural bases generating frequency can be observed throughout the mechanism purposes. The total structural modification can be performed in the x-y or z axes of the dipole configuration. The sensing of the acceleration management is organizing the testing properties in a sequential scenario. The ratio based on frequency generation can be modified in various adat processing procedures. The increment or the decrease in many occurrences can occur for the purpose of various graphical plots. The stimulation process can be done of the modification dynamically by the software-based designing language “Ansys”. The result collected from the dynamic analysis can be structured in a many-spectrum analysis.

3.8. Technical Aspects

A vibration or shock is common for a mechanical structure which is basically produced from the kinetic energy and caused several damages to the mechanical structure and the construction. Mechanical damage in the mechanical system can generate faults and also damage the manufacturing and processing components of the mechanical structure. Vibration attenuation features can be contained in shock absorbers, linear dampers, spring isolators, elastomeric isolators, air springs, or some mechanical damping treatments which helps the producers reduce equipment rest and cost limitations. This system can be used in a wide range of applications, from the construction field to the automobile mechanism and thereafter

In the field of farming, aircraft, GPS system, and many more where heavy equipment is used, vibration absorber systems are used to reduce mechanical and also natural vibration. Here most vibration absorbers conduct their damping aspects using hydraulic fluids which are forced by a piston and rod via small holes to produce damping, and therefore a compressed gas drove out from it (Auleley et al. 2021). This gas generates a spring pressure to push back the rod to its starting place when the pressure is released. Basically, the vibration absorbers are formed by high-strength steel to endure the pressure and save the mechanical structure from damage.

In the present day, the developer tries to construct an absorption system with longer service life and compact structure. Noise reduction techniques are now also added to the dynamic vibration absorber system to make the absorber more suitable and acceptable. A specific application for the vibration absorber devices has come with the improved awareness for environmental protection of our infrastructures like buildings, bridges, and many more. By adding damping to these structures, energy is absorbed by the hydraulic machines without damaging the mechanical structure.

An isolator is a very important thing for the vibration absorber and it is made from very high-strength materials like carbon steel, stainless steel, and others. Elastomeric isolator basically contains metallic components which provide the stiffness and proper damping for the vibration absorber. Most of the vibration absorber design is reusable and also self-contained which offers a lot of advantages and disadvantages to the mechanical structures.

Advantage

There is a lot of advantage to using a vibration absorber for a mechanical structure where it reduces the damage and failure rate. A vibration absorber particularly reduces vibration on machinery which reduces internal damage, maintenance costs, and downtime. Here absorber also increased the production rate and also provide a higher and smoothed momentum to the mechanical structure removing the moving object. An unnatural noise, vibrations, or damaging impact is very harmful to a mechanical structure and affects the product quality. Here the vibration absorber eliminated those motions which increased the product quality for mechanical machinery (TOMIOKA et al. 2021).

Simply saying a vibration absorber system provides longer lives, lower maintenance, and safe operations to the mechanical structure or the infrastructure.

Disadvantage

Being an important part of the mechanical structure there are some disadvantages to using the vibration absorber system. In the absorber when the forcing frequency is similar to the natural frequency of the central mass the comeback is infinite, which is called resonance, which is cause some problems for vibrating structures. The dynamic vibration absorber is performed only at a specific frequency that fits its resonant mode which is a major disadvantage for the vibration absorber. Here it is complicated to calculate numerically and also shows some problems when it applies to a nonlinear system. In the dynamic vibration absorber, PRV sometimes misleads the results and gives some errors.

3.9. ANSYS Simulation

Mass damping for a vibration absorber is manufactured in the ANSYS domain and the system. A damper is basically constructed by a mass block and a spring system for the compile the test. Here basically used some high-strength materials to develop the system because of its specific characteristics. Stainless steel, carbon steel, aluminum, and others are the main materials for developing the system because these materials are very good in energy consumption which is very important for the vibration absorption process (Qin et al. 2021).

1. Mesh analysis in ANSYS

Mesh analysis is the process of constructing 2D and 3D grids which simplifies the process of dividing the critical geometries to discretize a field. The mesh analysis in ANSYS makes progressive automatic mesh generation tools that can deliver faster and more accurate solutions for CFD which is a type of fluid and also FEA Meshing.

1. Model analysis in ANSYS

The model analysis is a basic dynamic study type that provides some natural frequency to the mechanical structure for resonating. This natural frequency is very important in the field of structural engineering because with the help of the natural frequency of the mechanical structure the engineers can differentiate it from the seismic waves or the fre4quency which was created by earthquakes and other natural disasters.

1. Harmonic analysis in ANSYS

In the construction field, the overload of the materials on the structures is very important for a vibration absorber. Here the ANSYS and the mechanical workbench can conduct a base acceleration in harmonic analysis on the mechanical structures. Basically, with the help of harmonic analysis, the response of the structure to the excessive load gives the proper solution to the infrastructure.

1. Transient analysis in ANSYS

Transient analysis is the process of measuring and defining the impacts of the loads and internal forces that are a process of time on a mechanical structure. Basically, it is used to specify the dynamic response of a mechanical structure under the movement of any time-dependent loads. Transient analysis generally depends on the DOFs involvement and is also solved by the appropriate procedure (Trujillo-Franco et al. 2022).

1. Static analysis in ANSYS

A static structural analysis computes the effect of continuous loading conditions on a structure while ignoring inactivity and damping effects, such as those generated by time-varying loads. Here a static analysis also defines the displacement, stresses, strains, and forces in the mechanical structure which is basically generated by the loads.

3.10. Process and steps involved in the design process adopted

The processing is the reflective implementation for the purpose of software analysis. The practical demonstration is constructed throughout the software analysis. There the implementation of the process can be done by the “Ansys” software, the purpose that, the building structure has to practically demonstrate that can resolve the damaging purposes (Ding & J, 2019). The structural damage can be minimized by setting the feature weise configuration for the purposes of 3d kind of modeling design in a technical representation to prevent the damage. Basically, the following configuration can be performed in various feature base element analyses for designing purposes. There are many other aspects like transferring the heat for the purposes of heat transferring methodological thermal analysis. There are many other perspectives that can be analyzed like buckling analysis to the bases of designing the vibrational resistance modeling processes (Tao).

The purposes of building construction the earthquake has impactful issues to damaging the structure, basic structure of the construction like several long bridges, and very large buildings, there mainly steel-based mixed construction phenomena is represented, so the represented analysis in the “Ansys” is reflecting the engineers to implementing feature wise element analysis called “FEA” to help the structural mechanism to resist the vibrational isolation. There are many functional analyses that can be done for the purpose of the mechanism of the modelling. The magnetostrictive approaches can be done through our designing purpose, the represented model is ambler to implement the resist the vibrational isolation effectively, and the controlling of the mechanical or thermal field has to be coupled dynamically to the purpose of transmitting the frequency dynamically (Luo et al. 2019 ). There are some vibrational problems that can occur in the cases of some overloaded vehicles or dumpers there is the high frequency of the vibrational force can be occurred so this kind of software-based analytics model can be applied for that purpose to resist the vibration.

Chapter 4: Results and analysis

4.1. Introduction

The represented analysis of optimizing the vibration resistance design, there are a rapid number of cycling synchronization that can be done, there are many topological folded models are reflected the management purpose, and there are many sets of dipole magnetic field orientation to accelerating the technical indexes to reduce the vibration, there are several factors can be observed to modeling the functionality. The common thing here for the objective purpose is to analyze the testing fundamentals in the bases of linear vibrations;l forms. The model of designing is mainly based on the finite element method to reflect the relative excitation in the bases of vibration that occurred. There are many factors that are performed to analyze the damping ratio on the bases of vibrational methodology to a dynamical characteristic to provide the vibration-free mechanism.

4.2. Implementation

The implementation of the represented vibration resistance optimization, “Ansys' ' are used to provide the simulation in multibody dynamical approaches. The “Ansys' ' is basically processing the electromagnetic noises in the perspective of the vibration; it can be structured as several graphical representations for the purposes of curve lines or line-based parameters. The geometrical approaches can be performed on the bases of connecting nodes, several piston analyses, and supportive objectives in the reflected coordinate system globally. The contact region can be analyzed in the bases of regional; analysis of the contract region of the bodies. The analysis of it can give the visualization of the contract body and the targeted body preferences. The analysis purpose occurred in the particle-wise analysis methodology in a structured way.

The analysis settings can visualize the static information to the providation og the solutional information. The several co ordinate wise visualization are can be done in the particular analyzing visualization. There are many structural analyses that can be performed to optimize the models. The structural analysis can be done for the purpose of density or the preferable isotropic elasticity of the particulars. There are many modulus derivations can be performed to measure the objective in a geometric plot. The thermal expansion can be implemented to figure out the ultimate strength ness in showcasing the line parameters.

The spring of the preferable representation can be used to utilize the particular aspect to provide the objectives of the vibration and required methodology to analyze vibration-free designing provision. The static analysis can be done in various aspects like the analysis of the settings of the particular particle on the bases of force-generating factors and the fixed support objectives. The solution of the vibrational purpose can be performed in dynamic analytics away from the abuses of formation analysis.

The equivalent strain can be observed elastically, and the strain energy should be measured to figure out the output. The represented model basically analyzes the finding elements to the various applications based on the dumper kind of overloaded vehicles to overcome the jerking purposes or like the large building to provide the vibrational free in the bases of occurring earthquakes the implementation of the model is beneficial to approach. There are many motion-based rotations ot\r the frequency generation properties that can be observed throughout the analysis for the purposes of occurring on the bases of the vibrational isolation. The structural mechanism can be displayed in the three-dimensional approaches to neutralize the vibrational occurrence in the structural purposes mechanism of the buildings or the overloaded dumper kinds of vehicles, the application of it is able to provide the vibration-free output modeling purposes.

4.3. Result and implementation

Figure 4.1: Structural Steel Characteristics

The picture attached above showcases a number of attributes that are linked to the structural steel in particular. The “strain-life parameters” and the “S-N Curve” are displayed in this section (Cirelli et al. 2019). Here, the values of “Tensile Ultimate Strength”, and “Tensile Yield Strength” are “4.6e⁺⁰⁸ Pa”, and “2.5e⁺⁰⁸ Pa” respectively. In case of the thermal properties, the parameters such as “Isotropic Thermal Conductivity”, and “Specific Heat Constant Pressure” are also shown. The values of the aforementioned parameters are “60.5 W/m-°C”, and 434 J/kg °C” respectively.

Figure 4.2: Contact Region and Analysis for Piston

In this image the connections have been made that are further displayed in the “Ansys” software platform. All of the contact regions have been connected with one another to form the entire shape of this element (Fernandez Escudero, 2021). The contact region in color “red” refers to the “Contact Bodies”, and the “blue” one refers to the “Target Bodies” respectively.

Figure 4.3: Analysis for spring

The figure and the parameters displayed in the above image refers to the aspect of geometric modeling and analysis in respect of the element “Spring”. The material which has been taken up for performing the model analysis is “Structural Steel” in this regard (Fuqing et al. 2022). The contact regions are connected in order to form the entire connection between all the individual layers.

Figure 4.4: Geometric Analysis of Piston

(Obtained from Ansys)

According to the above figure, a piston has been represented and the piston has seven contact regions. The contact regions depict the portions of the piston where external contact is experienced. Due to contact with external objects, the piston experiences an interaction with forces and the target body view of the piston has been shown alongside the piston. The figure represents Geometrical analysis of the piston that has been drawn using the software tool Ansys.

Figure 4.5: Finite Element Analysis and Mesh Analysis

(Collected from Ansys)

This particular image has been obtained after performing the finite element analysis. It is nothing but a particular process for simulating the overall behavior of a specific part or a whole assembly under the provided conditions (Javanshir et al. 2021). This in turn helps in simulating the required physical phenomena which reduces the requirement for the physical prototypes. The optimisation of all of the included components are also enabled in this regard as an element of the “design” process. Essentially, “FEA” utilizes the mathematical models for the purpose of comprehending and quantifying all the effects of the real-world conditions in respect of a part or an assembly.

All of these simulations that have been performed by way of the software platform “Ansys” help to locate all the potential issues within a particular design. This includes the weak spots as well as the tension areas respectively. The above element has been cut into a number of pieces and then joined together in the aforementioned software platform, at specific points known as nodes.

Moreover, the Mesh Analysis refers to the process of turning all of the irregular shapes into more understandable volumes, that are known by the name “elements” in this case (Kolyshev et al. 2019). It generally assists in bringing down the total quantity of effort and time spent in order to attain the results in an accurate manner.

Figure 4.6: Geometry of the Spring

(Retrieved from Ansys)

The material in this image is one of the many parts that has constituted the entire process of model analysis in respect of their geometric configuration (Li, 2021). All the contact regions along with corresponding connections are also displayed in this regard.

Figure 4.7: Analysis of Spring

(Obtained from Ansys)

The element in this picture above is a “spring” that has been a part of the geometric model analysis amongst other materials. The “7” regions of contact have also been displayed, by taking the assistance from “Ansys” software platform, that helps in forming the overall connection.

Figure 4.8: Parameters of Structural Steel

(Collected from Ansys)

The picture showcases a lot of crucial parameters that together describe the properties of the element in question. The density in this case is “7850 kg/m³”. The properties related to the isotropic elasticity of the concerned material has also been obtained with the help of the “Ansys” software platform (Lisitano, 2021). The values regarding some of the obtained parameters such as Bulk Modulus, Shear Modulus, Poisson’s Ratio are “1.667e⁺¹¹ Pa”, “7.6923e⁺¹⁰ Pa”, and “0.3” respectively.

Figure 4.9: Outcome of Solution

(Obtained from Ansys)

A spring has been depicted in the above figure and this spring has been used for geometric model analysis. The figure has been formed with the help of the software platform called Ansys. The strain energy of the spring has been studied for this assignment and the strain is the force which is exerted by the spring as a reaction to the load on the spring (Özyar, 2021). The different forces experienced by the spring consists of the equivalent elastic strain, Equivalent stress, and the strain energy generated from the spring. The spring has been created to scale using the software tool Ansys and the spring has been constructed using reliable material.

Figure 4.10: Solution Results

(Acquired from Ansys)

According to the above figure a spring has been depicted and it has been created using the software platform called Ansys. The spring is a part of the solution results that has been created using the software tool called Ansys (Pappalardo et al. 2018). The spring has been drawn to scale and the spring can be exerted to different forces which can be categorized into stress and strain. Load can be attached to the spring and the spring can feel strain forces due to the force exerted by the load. The spring has been constructed using reliable materials.

Figure 4.11: Solution Outcomes

(Collected from Ansys)

In the above figure, the solution outcomes created using the software tool called Ansys has been depicted. In the figure, a spring has been represented and the spring has been drawn to scale. The spring is subject to stress and strain and the spring is made of reliable material.

5. Conclusion & Future Recommendations

5.1. Conclusion

High degree of noise is very common when it comes to the interior of the aircrafts. This in turn brings about certain issues for the crews and the passengers, such as discomfort issues, speech interference etc. The comprehensive usage of the dynamic vibration absorber has proven to be of great value for the purpose of mitigating the noise levels in the aircraft’s interior. In case of material selection, aluminium has been prioritized over stainless steel so as to avoid a number of impediments regarding the aircraft. The ideal material has been a polymer called “Sorbothane” in this regard. Many degrees of freedom have been taken into consideration while implementing the damping vibration absorber. The frequency types are also taken into account as far as the functions of “DVA” are concerned.

5.2. Linking with Objectives

Linking with objective 1

A suitable model of a spring-mass damping vibration absorber is constructed inside “Ansys” Design Modeller.

Linking with objective 2

The overall performance level of the “DVA” is carefully evaluated by way of “Finite Element Analysis” within the software platform Ansys.

Linking with objective 3

A “three-dimensional” couple dynamic system is constructed with respect to the aspect of vibrational analysis through the Ansys “parametric” design language.

Linking with objective 4

The “vibration isolation” performance of the damping vibration absorber is determined while the dynamic and harmonic conditions of “loading” are in effect.

5.3. Recommendations

The benefits of “DVA” have been explained in the earlier sections (Pokhrel et al. 2020). Although the inconsistencies of the system in question have been elucidated, there also remains some crucial insights which need to be taken care of while using this system. The advantage of this system lies in its ability to reduce the vibration levels over a large range of frequencies. The area where this device is getting placed has to be considered with utmost importance as a lesser distance from the source of vibration can yield better performance in terms of the observed output. Here, only two degrees of freedom have been taken into consideration with respect to the damping vibration absorber system (Raze, 2021). But, in the ideal condition the system has to operate across multiple degrees of freedom in general.

5.4. Future Scope

Here, the use of aluminium has been specified as opposed to the use of stainless steel. As the former has better characteristics in respect of the required necessities, such as light weight, etc, it has been opted in this context (Tian et al. 2021). This material has the ability to bring down the factor called “bucking” by dint of having more thickness for that matter. But, for this system to showcase optimum results the polymer called “sorbothane” has to be used in almost all of the occasions. The sole reason for the aforementioned case is this material’s better performance in terms of the desired parameters which is light weight amongst others. This in turn helps in bringing down the energy level in the most efficient manner possible (Tishhenko et al. 2020). When it comes to the aircrafts, this system has to be mounted at the right place in relation to the airframe, so that most of the energy is absorbed without using up much of the resources.

5.5. Limitations

Here, there exists some key factors that have restricted the entire performance of the system up to a certain extent. The first one being the “suppression performance” that has been restricted to a specific limit. This in turn generates “resonant frequencies” within the system which need to be discarded in order for the system to perform in its optimum capacity (Xiao et al. 2019). The consideration of only “one” and “two” degrees of freedom are also an impediment in this case as far as the construction of a damping vibration absorber is concerned.

In reality, the existence of “multiple” degrees of freedom essentially enhances the underlying performance pertaining to the “DVA”. The inclusion of “un-damped” theory in terms of the calculation aspect has not been very convenient in this regard. Fundamentally, it needs the existence of an “optimization factor” for the purpose of addressing the real-world issue in general. The existence of “multiple” degrees of freedom generally increases the total quantity of elements existing inside of the absorber, resulting in a greater material weight. The solution with regards to the aforementioned issue is the incrpairing of pertinent material into the system that has been discussed earlier.

5.6. Summary

In this research project, the earlier mentioned software platforms have been for the sole purpose of constructing the design model of the “spring-mass” damping vibration absorber in particular. The efficiency in its performance has also been assessed through “Finite Element Analysis”. The loading conditions such as “harmonic”, and “dynamic” have been in force, in which the “vibration isolation” performance of the “DVA” has been decided.

The aspect of choosing the right material holds much significance in this case, because only the pertinent material can show the best outcome when it comes to the absorption of vibration. The inclusion of stainless steel has brought about a number of hindrances that have contributed to the overall performance of the “DVA”. The high amount of weight pertaining to the aforementioned material has increased the “bucking” factor. Whereas, the incorporation of aluminium has by far mitigated the vibration level by dint of having lesser weight than that of stainless steel. Aluminium also has an excellent ability to address the factor called “bucking”, as it has greater thickness. Another critical aspect is the “orientation” factor, which in turn facilitates the efficacy of the “DVA” in absorbing all of the vibrations.

References

• Rossato, B. B. and Miguel, L. F. (2021). Robust optimum design of tuned mass dampers for high-rise buildings subject to wind-induced vibration. Numerical Algebra, Control and Optimization, 2155-3289. doi:doi:10.3934/naco.2021060
• Rincón, C., Alencastre, J. and Rive, R. (2021). Active Vibration Absorber for a Continuous Structure Model. doi:10.31224/osf.io/r3ujn
• Wang, X., Liu, X., Shan, Y., Shen, Y. and He, T. (2018). Analysis and Optimization of the Novel Inerter-Based Dynamic Vibration Absorbers. IEEE Access, 6, 33169-33182. doi:10.1109/ACCESS.2018.2844086
• Lavazec, D., Cumunel, G., Duhamel, D. and Soize, C. (2017). Attenuation of acoustic waves and mechanical vibrations at low frequencies by a nonlinear dynamical absorber. Congrès Français de Mécanique (CFM 2017) (pp. 1-12). Lille: hal-01585746. Retrieved from https://hal-upec-upem.archives-ouvertes.fr/hal-01585746
• Kari, L. (2020). Are Single Polymer Network Hydrogels with Chemical and Physical Cross-Links a Promising Dynamic Vibration Absorber Material? A Simulation Model Inquiry. Materials, 13(5127), 1-19. doi:10.3390/ma13225127
• Richiedei, D., Tamellin, I. and Trevisani, A. (2022). Beyond the Tuned Mass Damper: a Comparative Study of Passive Approaches to Vibration Absorption Through Antiresonance Assignment. Archives of Computational Methods in Engineering,29, 519-544. doi:10.1007/s11831-021-09583-w
• Zhou, S., Mistral, C. J. and Chesne, S. (2019). Closed-form solutions to optimal parameters of dynamic vibration absorbers with negative stiffness under harmonic and transient excitation. International Journal of Mechanical Sciences, 157-158, 528-541. doi:10.1016/j.ijmecsci.2019.05.005
• Sayyed, A. B., Sonar, G., Suryawanshi, K., Shaikh, M. G. and Taware, S. (2020). Design and Analysis of Tune Mass Damper System. International Journal of Engineering Research & Technology (IJERT), 9(10), 588-591.
• Özer, A., Ghodsi, M., Sekiguchi, A., Saleem, A. and Al-Sabari, M. N. (2015). Design and Experimental Implementation of a Beam-Type Twin Dynamic Vibration Absorber for a Cantilevered Flexible Structure Carrying an Unbalanced Rotor: Numerical and Experimental Observations. Shock and Vibration, 2015, 1-9. doi:10.1155/2015/154892
• Chai, C. S. and Ko, Y. H. (2021). Design and Experimental Implementation of a Passive Dynamic Vibration Absorber to Attenuate Broadband Vibration. Journal of Physics: Conference Series, 2051, 1-7. doi:10.1088/1742-6596/2051/1/012020
• Sriramdas, R., Rastogi, S. and Pratap, R. (2016). Design Considerations for Optimal Absorption of Energy from a Vibration Source by an Array of Harvesters. Energy Harvesting and Systems, 3(2), 121–131. doi:10.1515/ehs-2015-0021
• Teik, H. S. (2013). DESIGN OF A DYNAMIC VIBRATION ABSORBER. Melaka: Universiti Teknikal Malaysia.
• Harik, R. F. and Issa, J. S. (2013). Design of a vibration absorber for harmonically forced damped systems. Journal of Vibration and Control, 0(0), 1-11. doi:10.1177/1077546313501928
• Luan, S., Arora, M., Thurston, D. L. and Allison, J. T. (2017). DEVELOPING AND COMPARING ALTERNATIVE DESIGN OPTIMIZATION FORMULATIONS FOR A VIBRATION ABSORBER EXAMPLE. ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (pp. 1-12). Cleveland: IDETC/CIE 2017.
• Yoon, G. H., Choi, H. and So, H. (2021). Development and optimization of a resonance-based mechanical dynamic absorber structure for multiple frequencies. Journal of Low Frequency Noise, 40(2), 880-897. doi:10.1177/1461348419855533
• Singh, A. P., Sharma, D., Chouhan, J., Shankhwar, K., Thakur, K., Javre, P. and Pande, V. (2012). DYNAMIC VIBRATION ABSORBER. Bhopal: Rajiv Gandhi Proudyogiki Vishwavidyalaya.
• Desen, I. C. (2000). EXPERIMENTAL STUDY ON AN IMPACT VIBRATION ABSORBER. Texas: Texas Tech University.
• Harel, S. S. (2017). FREQUENCY TUNING OF VIBRATION ABSORBER USING TOPOLOGY OPTIMIZATION. Arlington: The University of Texas at Arlington.
• Monkova, K., Vasina, M., Zaludek, M., Monka, P. P. and Tkac, J. (2021). Mechanical Vibration Damping and Compression Properties of a Lattice Structure. Materials, 14(1502), 1-16. doi:10.3390/ma14061502
• Broch, J. T. (1984). Mechanical Vibration and Shock Measurements. NÆRUM: K. LARSEN & SON A/S.
• Naucler, P. (2005). Modeling and Control of Vibration. Uppsala: UPPSALA UNIVERSITY.
• Taflanidis, A. A., Giaralis, A. and Patsialis, D. (2019). Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures. Journal of The Franklin Institute, 1-36. doi:10.1016/j.jfranklin.2019.02.022
• Carbajal, F. B., Badillo, H. Y., Olvera, R. T., Contreras, A. F., Gonzalez, A. V. and Garcia, I. L. (2022). On Active Vibration Absorption in Motion Control of a Quadrotor UAV. Mathematics, 10(235), 1-25. doi:10.3390/math10020235
• Hua, Y., Wong, W. and Cheng, L. (2018). Optimal design of a beam-based dynamic vibration absorber using fixed-points theory. Journal of Sound and Vibration, 421, 111-131. doi:10.1016/j.jsv.2018.01.058
• Li, Y., Lombardi, L., Luca, F. D., Farbiarz, Y., Blandon, J. J., Lara, L. A., . . . Neild, S. (2019). Optimal design of inerter-integrated vibration absorbers for seismic retrofitting of a high-rise building in Colombia. Journal of Physics: Conference Series, 1264, 1-12. doi:10.1088/1742-6596/1264/1/012031
• Piccirillo, V., Tusseta, A. M. and Balthazara, J. M. (2019). OPTIMIZATION OF DYNAMIC VIBRATION ABSORBERS BASED ON EQUAL-PEAK THEORY. Latin American Journal of Solids and Structures, 16(4), 1-22. doi:10.1590/1679-78255285
• Rade, D. A. and Steffen, V. J. (2000). OPTIMISATION OF DYNAMIC VIBRATION ABSORBERS OVER A FREQUENCY BAND. Mechanical Systems and Signal Processing, 14(5), 679-690. doi:10.1006/mssp.2000.1319
• Diveyev, B., Hlobchak, M., Martyn, V. and Yavorskyy, Y. (2015). OPTIMIZATION OF IMPACT DYNAMIC VIBRATION. Lviv: Lviv National Polytechnic University.
• ARAZ, O. and KAHYA, V. (2021). OPTIMIZATION OF NON-TRADITIONAL TUNED MASS DAMPER FOR DAMPED STRUCTURES UNDER HARMONIC EXCITATION. Bursa Uluda? University Journal of The Faculty of Engineering, 26(3), 1021-1034. doi:10.17482/uumfd.878114
• Zhu, X., Chen, Z. and Jiao, Y. (2018). Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates. Journal of Low Frequency Noise, 37(4), 1188-1200. doi:10.1177/1461348418794563
• Saadabad, N. A., Moradi, H. and Vossoughi, G. R. (2019). Optimized design of adaptable vibrations suppressors in semi-active control of circular plate vibrations. Scientia Iranica Transactions B: Mechanical Engineering, 26(3), 1358{1377. doi:10.24200/sci.2018.20417
• Pachpute, A. Z. and Bawa, P. B. (2016). Optimum Design of Damped Dynamic Vibration Absorber – A Simulation Approach. International Journal of Recent Engineering Research and Development (IJRERD), 01(02), 19-21.
• Mayer, D. and Herold, S. (2018). Passive, Adaptive, Active Vibration Control, and Integrated Approaches. IntechOpen. doi:10.5772/intechopen.71838
• Krenk, S. (2019). Resonant inerter based vibration absorbers on flexible structures. Journal of the Franklin Institute, 356, 1-30. doi:10.1016/j.jfranklin.2018.11.038
• Pani, S., Senapati, S. K., Patra, K. C. and Nath, P. (2017). Review of an Effective Dynamic Vibration Absorber for a Simply Supported Beam and Parametric Optimization to Reduce Vibration Amplitude. International Journal of Engineering Research and Application, 7(7), 49-77. doi:10.9790/9622-0707034977
• Au-Yeung, K. Y., Yang, B., Sun, L. and Ba, K. (2019). Super Damping of Mechanical Vibrations. Scientific Reports nature research, 9, 1-10. doi:10.1038/s41598-019-54343-3
• Dogan, H., Sims, N. D. and Wagg, D. J. (2020). THE EFFECTS OF PARASITIC MASS ON THE PERFORMANCE OF INERTER-BASED DYNAMIC VIBRATION ABSORBERS. In M. Papadrakakis, M. Fragiadakis, & C. Papadimitriou (Ed.), EURODYN 2020: Proceedings of the XI International Conference on Structural Dynamics (pp. 1545-1555). Athens: European Association for Structural Dynamics (EASD). doi:10.47964/1120.9125.19507
• Aksoy, T. (2015). TUNED VIBRATION ABSORBER DESIGN FOR A SUPPORTED HOLLOW CYLINDRICAL STRUCTURE. Ankara: MIDDLE EAST TECHNICAL UNIVERSITY.
• Bouna, H. S. and Nbendjo, B. R. (2012). Vibration Control of a Plate Subjected to Impulsive Force by Plate-Type Dynamic Vibration Absorbers. World Journal of Mechanics, 2, 143-151. doi:10.4236/wjm.2012.23017
• Wang, Q., Senatore, G., Jansen, K., Habraken, A. and Teuffel, P. (2020). Vibration Suppression Through Variable Stiffness and Damping Structural Joints. Frontiers in Built Environment, 6, 1-22. doi:10.3389/fbuil.2020.550864
• Chen, J., Chen, M. Z. and Hu, Y. (2021). Vortex-Induced Vibration Suppression of Bridges by Inerter-Based Dynamic Vibration Absorbers. Shock and Vibration, 2021, 1-18. doi:10.1155/2021/4431516
• Rubio, L., Loya, J. A., Miguélez, M. H. and Fernández-Sáez, J. (2013). Optimization of passive vibration absorbers to reduce chatter in boring. Mechanical Systems and Signal Processing, 41(1-2), 691-704. doi:10.1016/j.ymssp.2013.07.019
• Karam, M. A., Rezazadeh, G. and Ghaffari, S. (2015). An Investigation on Optimal Designing of Dynamic Vibration Absorbers Using Genetic Algorithm. Science Journal, 36, 765-779. Retrieved from https://www.researchgate.net/publication/286882651_An_Investigation_on_Optimal_Designing_of_Dynamic_Vibration_Absorbers_Using_Genetic_Algorithm
• Karimi, M., Shemshadi, M. and Firoozfam, N. (2020). A Simple method to design and analyze dynamic absorber using dimensional analysis. Journal of Vibration and Control,1(2), 73-81. doi:10.1177/1077546320923928
• Chesne´, S. (2021). Hybrid skyhook mass damper. Mechanics & Industry, 22(49), 1-10. doi:10.1051/meca/2021050
• EsmaiIzadeh, E. and Jalilj, N. (1998). Optimum Design of Vibration Absorbers for Structurally Damped Timoshenko Beams. Journal of Vibration and Acoustics,120, 833-841.
• Hu, Y. and Chen, M. Z. (2015). Performance evaluation for inerter-based dynamic vibration absorbers. International Journal of Mechanical Sciences,99, 297-307. doi:10.1016/j.ijmecsci.2015.06.003
• ASAMI, T., & YAMADA, K. (2021). Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞, H2, or stability criterion.Mechanical Engineering Journal,8(5), 21-00189. Retrieved on: 18/11/2022, Retrieved from: https://www.jstage.jst.go.jp/article/mej/8/5/8_21-00189/_pdf
• Feudo, S. L., Touzé, C., Boisson, J., & Cumunel, G. (2019). Nonlinear magnetic vibration absorber for passive control of a multi–storey structure.Journal of Sound and Vibration,438, 33-53. Retrieved on: 18/11/2022, Retrieved from: https://hal.archives-ouvertes.fr/hal-01891645/file/Lo_Feudo_et_al_2018V_revised_HAL.pdf
• Ha, S. I., & Yoon, G. H. (2021). Numerical and experimental studies of pendulum dynamic vibration absorber for structural vibration.Journal of Vibration and Acoustics,143(1). Retrieved on: 18/11/2022, Retrieved from: https://asmedc.silverchair.com/vibrationacoustics/article-pdf/143/1/011013/6559273/vib_143_1_011013.pdf
• Hua, Y., Wong, W., & Cheng, L. (2018). Optimal design of a beam-based dynamic vibration absorber using fixed-points theory.Journal of Sound and Vibration,421, 111-131. Retrieved on: 18/11/2022, Retrieved from: https://www.polyu.edu.hk/researchgrp/chengli/assets/pdf/197.pdf
• Infante, F., Kaal, W., Perfetto, S., & Herold, S. (2018, September). Design development of rotational energy harvesting vibration absorber (R-EHTVA). InSmart Materials, Adaptive Structures and Intelligent Systems(Vol. 51951, p. V002T07A001). American Society of Mechanical Engineers. Retrieved on: 18/11/2022, Retrieved from: https://www.researchgate.net/profile/Francesco-Infante/publication/327830955_Design_development_of_Rotational_Energy_Harvesting_Vibration_Absorber_R-EHTVA/links/5ba77597299bf13e60464f4a/Design-development-of-Rotational-Energy-Harvesting-Vibration-Absorber-R-EHTVA.pdf
• Ji, H., Zhao, X., Wang, N., Huang, W., Qiu, J., & Cheng, L. (2022). A Circular Eccentric Vibration Absorber With Circumferentially Graded Acoustic Black Hole Features.Journal of Vibration and Acoustics,144(2), 021014. Retrieved on: 18/11/2022, Retrieved from: https://www.researchgate.net/profile/Wei-Huang-199/publication/357715924_A_Circular_Eccentric_Vibration_Absorber_With_Circumferentially_Graded_Acoustic_Black_Hole_Features/links/61e12475c5e31033759184dd/A-Circular-Eccentric-Vibration-Absorber-With-Circumferentially-Graded-Acoustic-Black-Hole-Features.pdf
• Lang, Y., Tian, X., Kai, Y., & Hou, E. (2020, November). Stiffness and Mode Analysis of Framework for an Aerial Inertial Stabilized Platform. InJournal of Physics: Conference Series(Vol. 1635, No. 1, p. 012022). IOP Publishing. Retrieved on: 18/11/2022, Retrieved from: https://iopscience.iop.org/article/10.1088/1742-6596/1635/1/012022/pdf
• Luo, W., Lu, B., Zheng, H., Guo, Y., & Huang, T. (2019). A research of spinning machine: Effect of different structures of feed system on the static and dynamic characteristics.Advances in Mechanical Engineering,11(2), 1687814019828451. Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1687814019828451
• Noori, B., Arcos, R., Clot, A., & Romeu, J. (2019). Control of ground-borne underground railway-induced vibration from double-deck tunnel infrastructures by means of dynamic vibration absorbers.Journal of Sound and Vibration,461, 114914. Retrieved on: 18/11/2022, Retrieved from: https://upcommons.upc.edu/bitstream/handle/2117/174712/Noori,%20Behshad.%20Control%20of%20ground-borne%20underground%20railway-induced%20vibration%20from%20double-deck%20tunnel%20infrastructures%20by%20means%20of%20dynamic%20vibration%20absorbers.pdf?sequence=1
• Roozen, N. B., Urban, D., Piana, E. A., & Glorieux, C. (2021). On the use of dynamic vibration absorbers to counteract the loss of sound insulation due to mass-spring-mass resonance effects in external thermal insulation composite systems.Applied Acoustics,178, 107999. Retrieved on: 18/11/2022, Retrieved from: https://hal.archives-ouvertes.fr/hal-03202436/document
• Yang, F., Sedaghati, R., & Esmailzadeh, E. (2022). Vibration suppression of structures using tuned mass damper technology: A state-of-the-art review.Journal of Vibration and Control,28(7-8), 812-836. . Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1077546320984305
• Yoon, G.H., Choi, H. and So, H., 2021. Development and optimization of a resonance-based mechanical dynamic absorber structure for multiple frequencies.Journal of Low Frequency Noise, Vibration and Active Control,40(2), pp.880-897. Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1461348419855533
• Lang, Y., Tian, X., Kai, Y., & Hou, E. (2020, November). Stiffness and Mode Analysis of Framework for an Aerial Inertial Stabilized Platform. In Journal of Physics: Conference Series (Vol. 1635, No. 1, p. 012022). IOP Publishing.
• retrieve from: https://iopscience.iop.org/article/10.1088/1742-6596/1635/1/012022/pdf
• Luo, W., Lu, B., Zheng, H., Guo, Y., & Huang, T. (2019). A research of spinning machine: Effect of different structures of feed system on the static and dynamic characteristics. Advances in Mechanical Engineering, 11(2), 1687814019828451.
• retrieve from: https://journals.sagepub.com/doi/pdf/10.1177/1687814019828451
• Dai, L., Sun, H., Zhao, X., Wang, B., & Cao, J. (2021). Research on the Force Characteristics and Structural Optimization of Mine Antioutburst Door under the Influence of Coal and Gas Outburst Impact Airflow. Geofluids, 2021.
• retrieve from: https://www.hindawi.com/journals/geofluids/2021/5552949/
• ATLIHAN, G., OVALI, ?., & Abdullah, E. R. E. N. (2021). EKLEMEL? ?MALAT YÖNTEM?YLE ÜRET?LM?? BAL PETEKL? YAPILARIN T?TRE??M DAVRANI?LARININ NÜMER?K VE DENEYSEL OLARAK ?NCELENMES?. International Journal of 3D Printing Technologies and Digital Industry, 5(2), 98-108.
• retrieve from: https://dergipark.org.tr/en/download/article-file/1675731
• Bahrami, M. R., & Abed, S. A. (2019). Mechanics of robot inspector on electrical transmission lines conductors: performance analysis of dynamic vibration absorber. Vibroengineering Procedia, 25, 60-64. retrieve from: https://www.extrica.com/article/20807
• You, T., Zhou, J., Thompson, D. J., Gong, D., Chen, J., & Sun, Y. (2022). Vibration reduction of a high-speed train floor using multiple dynamic vibration absorbers. Vehicle System Dynamics, 60(9), 2919-2940.
• retrieve from:https://www.tandfonline.com/doi/full/10.1080/00423114.2021.1928248
• ASAMI, T., & YAMADA, K. (2021). Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞, H2, or stability criterion. Mechanical Engineering Journal, 8(5), 21-00189, retrieved from: https://www.jstage.jst.go.jp/article/mej/8/5/8_21-00189/_pdf
• Love, J. S., & Morava, B. (2021). Practical Experience with Full-scale Performance Verification of Dynamic Vibration Absorbers installed in Tall Buildings. International Journal of High-Rise Buildings, 10(2), 85-92, retrieved from: https://www.koreascience.or.kr/article/JAKO202117457616224.pdf
• Auleley, M., Thomas, O., Giraud-Audine, C., & Mahé, H. (2021). Enhancement of a dynamic vibration absorber by means of an electromagnetic shunt. Journal of Intelligent Material Systems and Structures, 32(3), 331-354, retrieved from: https://sam.ensam.eu/bitstream/handle/10985/22639/LISPEN_JIMSS_2020_THOMAS.pdf?sequence=2&isAllowed=y
• TOMIOKA, T., & HIGUCHI, K. (2021). Proposal and numerical feasibility study of a novel multi-modal and multi-axis dynamic vibration absorber consists of spherical viscoelastic material containing embedded ball-like mass. Mechanical Engineering Journal, 8(4), 21-00145, retrieved from: https://www.jstage.jst.go.jp/article/mej/8/4/8_21-00145/_pdf
• Qin, Y., Tan, J. J., & Hornikx, M. (2021, October). Reduction of low-frequency vibration of joist floor structures by multiple dynamic vibration absorbers: comparison of experimental and computational results. In Proceedings of Euronoise, retrieved from: http://ftp.sea-acustica.es/fileadmin/Madeira21/ID117.pdf
• Trujillo-Franco, L. G., Flores-Morita, N., Abundis-Fong, H. F., Beltran-Carbajal, F., Dzul-Lopez, A. E., & Rivera-Arreola, D. E. (2022). Oscillation Attenuation in a Building-like Structure by Using a Flexible Vibration Absorber. Mathematics, 10(3), 289, retrieved from: https://www.mdpi.com/2227-7390/10/3/289/pdf
• Cirelli, M., Gregori, J., Valentini, P. P., & Pennestrí, E. (2019). A design chart approach for the tuning of parallel and trapezoidal bifilar centrifugal pendulum. Mechanism and Machine Theory, 140, 711-729. Retrieved on: 19/11/2022, Retrieved from: https://www.researchgate.net/profile/Ettore-Pennestri/publication/334194064_A_Design_Chart_Approach_for_the_Tuning_of_Parallel_and_Trapezoidal_Bifilar_Centrifugal_Pendulum/links/5d1c6add458515c11c0ccb27/A-Design-Chart-Approach-for-the-Tuning-of-Parallel-and-Trapezoidal-Bifilar-Centrifugal-Pendulum.pdf
• Fernandez Escudero, C. (2021). Passive Aeroelastic control of aircraft wings via nonlinear oscillators (Doctoral dissertation, Polytechnique Montréal). Retrieved on: 19/11/2022, Retrieved from: https://publications.polymtl.ca/6578/1/2021_ClaudiaFernandezEscudero.pdf
• Fuqing, L., Chuanqiang, G., Zhen, L., Weiwei, Z., & Qiannan, X. (2022). Transonic flutter suppression with tuned mass damper by model-based stability analysis method. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 09544100221089704. Retrieved on: 19/11/2022, Retrieved from: https://www.researchgate.net/profile/Fuqing-Luo/publication/361984421_Transonic_flutter_suppression_with_tuned_mass_damper_by_model-based_stability_analysis_method/links/62cfe6147156f534a68299f7/Transonic-flutter-suppression-with-tuned-mass-damper-by-model-based-stability-analysis-method.pdf
• Javanshir, I., & Zarepour, G. (2021). Vibration analysis of fluid-structure interaction using tuned mass dampers. Journal of Applied Engineering Science, 19(2), 318-326. Retrieved on: 19/11/2022, Retrieved from: https://aseestant.ceon.rs/index.php/jaes/article/download/26043/16429
• Kolyshev, E. S., & Krapivko, A. V. (2019). Development of Computational and Experimental Methods for Determining Dynamic Characteristics of Aircraft Landing Gear. Retrieved on: 19/11/2022, Retrieved from: https://www.eucass.eu/doi/EUCASS2019-0502.pdf
• Li, L. (2021). Aircraft Noise Reduction Design Approaches (Doctoral dissertation, National Aviation University). Retrieved on: 19/11/2022, Retrieved from: https://dspace.nau.edu.ua/bitstream/NAU/55400/1/ASF_2021_134_LiLinfeng.pdf
• Lisitano, D., Bonisoli, E., Recchiuto, C. T., & Muscolo, G. G. (2021). Dynamic balance of the head in a flexible legged robot for efficient biped locomotion. Applied Sciences, 11(7), 2945. Retrieved on: 19/11/2022, Retrieved from: https://www.mdpi.com/2076-3417/11/7/2945/pdf
• Özyar, O., & Y?lmaz, Ç. (2021). A self-tuning adaptive-passive lever-type vibration isolation system. Journal of Sound and Vibration, 505, 116159. Retrieved on: 19/11/2022, Retrieved from: http://venus.santafe-conicet.gov.ar/ojs/index.php/mc/article/viewFile/6287/6353
• Pappalardo, C. M., & Guida, D. (2018). Development of a New Inertial-based Vibration Absorber for the Active Vibration Control of Flexible Structures. Engineering Letters, 26(3). Retrieved on: 19/11/2022, Retrieved from: http://www.engineeringletters.com/issues_v26/issue_3/EL_26_3_11.pdf
• Pokhrel, P. R., Lamsal, B., Kafle, J., & Kattel, P. (2020). Analysis of displacement of vibrating of mass spring due to opposition force. Tribhuvan University Journal, 35(1), 21-32. Retrieved on: 19/11/2022, Retrieved from: https://www.nepjol.info/index.php/TUJ/article/view/35830/28014
• Raze, G. (2021). Piezoelectric digital vibration absorbers for multimodal vibration mitigation of complex mechanical structures. Retrieved on: 19/11/2022, Retrieved from: https://orbi.uliege.be/bitstream/2268/256608/1/PhDThesis_GRaze.pdf
• Tian, W., Zhao, T., & Yang, Z. (2021). Metastructure plate with periodically embedded nonlinear vibration absorbers for nonlinear aeroelastic suppression. Retrieved on: 19/11/2022, Retrieved from: https://www.researchsquare.com/article/rs-364180/latest.pdf
• Tishhenko, I. V., Nikolaev, V. S., & Merkulov, V. I. (2020). Experimental study of the aircraft air cycle machine rotor dynamics on gas foil bearings. In MATEC Web of Conferences (Vol. 324, p. 03001). EDP Sciences. Retrieved on: 19/11/2022, Retrieved from: https://www.matec-conferences.org/articles/matecconf/pdf/2020/20/matecconf_cryogen2020_03001.pdf
• Xiao, X., He, Z. C., Li, E., & Cheng, A. G. (2019). Design multi-stopband laminate acoustic metamaterials for structural-acoustic coupled system. Mechanical Systems and Signal Processing, 115, 418-433. Retrieved on: 19/11/2022, Retrieved from: https://research.tees.ac.uk/ws/files/6455840/Design_multi_stopband_laminate_acoustic_metamaterials_for_structural_acoustic.pdf
• Appendix 1: Gantt chart

Appendix 2: Project Schematic

Outcome of the solution

Prarameters of the structured steel

1. Introduction Overview of Dynamic Vibration Absorbers in Mechanical Systems

The aim of this work is to design and optimise a dynamic vibration absorber which can be used to reduce the mechanical vibration in mechanical structures on which they are installed. Dynamic Vibration Absorbers (DVAs) are passive equipment mounted in mechanical systems to reduce the vibration of the mechanical structure at certain frequencies. A mass – damper – spring system is used as the basic motion damping block in a mechanical system (Broch, 1984). The initial damping systems developed never had a damping element, but instead had a secondary mass element which was attached to the principal mass using a secondary spring (Broch, 1984). This absorber was effective in a constrained range of frequencies which are closer to the natural frequency of the principal system (Broch, 1984). This type of system is capable of reducing vibrations having frequencies which are closer to the natural frequency range of the main system to which the absorber is attached (Broch, 1984). But when resonant frequency vibrations occur such systems are not capable of attenuating such frequencies and this type of system is called tuned mass damper system. This work is aimed at developing a dynamic vibration absorber for reducing mechanical vibrations.

The term “Dynamic Vibration Absorber” is also known by the names “Tuned Mass Dampers”, and “Vibration Neutralizers” in general. This is a mechanical appendage which consists of inertia, damping elements, and stiffeners that are attached to the machine in question to absorb the energy of vibration at the point of connection. This helps the system in focus to stay protected from the extremely high degree of vibrations. In reality, the “DVA” can very well be incorporated into the design pertaining to the original system or the existing system by way of a remedial mode of action. Nowadays, the dynamic vibration absorbers are used extensively for the purpose of bringing down the vibration levels in different categories of mechanical systems. In case of the practical; applications, the dynamic vibration absorbers could be witnessed in different configurations which are intended to reduce the angular or rectilinear motion for that matter.

1.1. Project Aim

The sole aim of this particular project is to construct and develop a “Dynamic Vibration Absorber” to reduce the mechanical vibrations in case of a continuous structure by way of “Finite Element Analysis” in “Matlab”, and “Ansys”.

1.2. Project Objectives

• To create a suitable model of “DVA” within “Matlab”, and “Ansys” Design Modeler
• To thoroughly evaluate the performance level regarding the “DVA” with the help of “Finite Element Analysis” inside Ansys
• To bring about a “three-dimensional” coupled dynamic in respect of vibrational isolation by way of the “parametric” design language called Ansys
• To determine the “vibration isolation” performance pertaining to the “DVA” provided that the harmonic and dynamic conditions of loading are in effect

1.3. Background

The dynamic vibration absorbers are essentially attached to the host structure for controlling the motion. These types of devices are used rapidly for controlling the vibration ensuing from the aircraft frameworks (Roozen et al. 2021). The operation of this type of device depends on the manner in which their application takes place. One of the ways to operate this type of device is to suppress the underlying vibration at a specific “forcing frequency”. In such cases the natural frequency of the device gets tuned to the excitation frequency. The damping factor pertaining to the concerning device is to be low in particular, for rendering the most amount of resistance to the underlying framework at the “operating frequency”.

This particular device gets known by the name of “vibration neutralizer” in general. Moreover, this device can also be used for mitigating the vibration produced from a specific mode of structure across a set of frequencies. In this case, the device gets known as “Dynamic Vibration Absorber”. The ratio of damping along with the optimum tuning regarding the natural frequency of the concerning device becomes less prominent. It is also predicted on the manner in which the criteria optimization gets defined.

1.4. Scope of the Research

In the case of aircrafts, it is extremely crucial to ensure the stability of the aircraft so that the degree of comfort and convenience remains top-notch. This would not only render a hospitable environment for the crews but for the passengers as well. In the context of this research, it is very obvious to consider the dynamic vibration absorbers by way of the way they are incorporated in the aircraft's frame (Yang et al. 2022). The usage of these damping absorbers is rising day by day as far as the place of application is concerned. In the aerospace industry, any slight deviation from the ideal condition of the aircraft parameters can bring harmful outcomes. Vibration, which if goes above a limited range can tamper with the aircraft's performance, resulting in the degradation of passenger experience. So, it can very well be predicted based on the present scenario that the application of such absorbers will not only go up in quantity but also in clarity too for that matter.

1.5. Themes

Damping vibration absorber essentially eliminates all of the unwanted vibrations that are produced inside of any system. It comprises an auxiliary system along with an attached “absorber mass” which constitutes a system having “2 degrees of freedom”. It is obvious for this type of system to have two types of natural frequencies based upon its objective of application. The spring mass “DVA '' in this case operates across a range of narrow frequencies and also suffers from deterioration in performance owing to the change in excitation frequency (Yoon et al. 2021). The introduction of the factor of damping helps to enhance the robustness of performance. In comparison to the un-damped “DVA”, damped “DVA” has got lower response along with increased range of operational frequency.

1.6. Dissertation Plan

This particular Dissertation is structured in the following manner:

Chapter 1: This chapter deals with the introduction part which illustrates the very concept and workings of the Dynamic Vibration Absorber. The aims as well as objectives are also explained along with the aforementioned part.

Chapter 2: In this chapter the focus is on the Literature review. This chapter thoroughly analyzes the previously performed works, existing gaps in the literature, along with elaborating on the crux of the issue.

Chapter 3: This chapter is known by the name Methodology, which lists out all of the techniques and approaches that are abode by to bring a solution to the issue in question.

Chapter 4: This particular chapter deals with the aspect of simulation inside the platform of Matlab. The results obtained from creating a “Mass” spring damper having a 3-degree or 2-degree freedom is also discussed.

Chapter 5: In this chapter, the simulation aspect inside the Ansys platform is taken into consideration. All of the related results are also discussed in relation to an “un-damped” system having “2-degree” freedom.

Chapter 6: This section explains in brief regarding all that have been performed in this research project in general.

Chapter 7: This chapter consists of a set of recommendations that are useful in the case of further developing this project in the long run.

The Appendices along with the Gantt chart are also included at the end of the final chapter in order to execute the project timeline as well as project schematic respectively.

2. Literature Review

The performance of mechanical systems is affected negatively by vibrations which might lead to equipment damage, energy loss, and mechanical parts erosion and so on. Composite materials have been used extensively in various applications of research and engineering especially in the recent development within the aerospace industry, submarine and automotive structures. This is due to the high strength to stiffness ratio and light weight structure they have when compared to other metallic materials. These highlight their merits along with their potential to be customised and tailor designed for achieving specific design parameters with lower weight and increased strength. Composite vibration analysis is a major challenge in composite structural design.

The vibration absorber mechanism of any mechanical structure is the base support that protects the total mechanical structure from any sort of accident. Without proper support from the vibration absorber, big mechanical structures like bridges, vehicles, and aircraft are unable to avoid great disasters and accidents. The research in the field of improving new models of vibration absorbers is still going on and many innovative designs are coming into the market. The vibrations absorbers is supporting all the mechanical structures in as many ways as possible. For big structures like in the case of bridges, the “Stock bridge damper” is used as a vibration absorber which is a “TMD (Tuned Mass Damper)”.

This absorbing mechanism for the bridges can suppress the induced wind vibration on the slender structures of the bridge like the power cables of the bridges, “long cantilevered signs” and “the cable-stayed bridges”. The vibration absorption system for the vehicles is the main suspension mechanism of the vehicle with the “torsional vibration damper” also used for absorbing all the rotational vibrations for the “IC engines”. In the case of the aircraft, the vibration absorption is done by the “turbofan operator” and with the help of simple maintenance by the “turbofan operator,” the engine vibration of the airplane can be kept under control. The topic is mainly about the design and makes optimization of the “Dynamic vibration absorber” which is also known by the name of “Tuned mass Dampers”.

2.1. Background

The concept of the “Dynamic vibration absorber” is first applied by “Frahm” in the year of 1909. By using this concept the rolling motion of the ships along with the ship hull vibrations. A research paper on the topic of TMD was published later in the year of 1928 by “Ormondroyd and Den Hartog”. After this research, the next paper includes a detailed discussion on the topic of “optimal tuning” and parameters related to the damping vibrations published in the year 1940 by “Den Hartog”.

The earlier research on this topic is about “Frahm's undamped SDOF system” which is caused by the force of sinusoidal excitation. Another researcher name “Brook” in the year of 1946 took a different path in research which is a more efficient method for improving the field of developing dynamic vibration absorbers. The method does not consist of differentiation methods and from the research results the ratio of the optimum damping model is implemented in this research. Another researcher named “Srinivasan” researched this optimized parameter of the damping ratio for designing a parallel damped “dynamic vibration absorber or (DVA)” in the year of 1969.

Figure 1: Damped Dynamic Vibration Absorber Model

(Source: Gong et al. 2022)

Another research paper which is published in the year of 2004 by “Kefu liu and Jieliu” provides a model of the optimized parameters ratio of the “damped dynamic vibration absorbers”. Another part of this research is about the “SDOF systems” and this research on these “SDOF systems” is conducted by many researchers. By using the external power supply the “active control devices” can operate easily so these “active control operators” are much more efficient than the “passive control devices”. However, problems arise when “control-force capacity” becomes insufficient and a huge power supply is required in the current technology of the structural control for countering against the high scale earthquakes. These problems are the major issues in the modern technology of the “DVA” that needs to be overcome. To solve this problem a technical solution is available in the market which can use both active and passive control devices.

The name of this new control device is “semi-active control device” and it is very attractive in the market because of its very low power consumption and proper stability. The previous research papers are about the topic of “SATMD” and this research is done in the year 1983. The researcher presents the “SATMD”, and “TMD” which is controllable damping that includes time variation.

In the case of identical conditions, the behavior of the “SATMD” instead of the “TMD” is more efficient considering the structural control.

2.2. Description and comparison of the approaches undertaken

The definition of the “DVA or dynamic vibration absorber” can be explained as the “DVA” is the conjunction of a “tuned-spring mass system”. Using this system the vibration or the shockwaves of a mechanical structure can be eliminated or reduced. The invention of the “DVA” is done by the researcher” Hermann Frahm” in the year of 1909 after that, the “DVA” was used to suppress the vibrations induced by the wind and reduce the “seismic response” for buildings. The “SATMD” control design system is not suitable for the parameters like mass, ratio, and frequency. The structure with TMD is tuned for first-mode response in the fundamental frequency of the mechanical structure.

For overcoming the problems related to the frequency in the case of using one “TMD” so more than one “TMD” is installed in the mechanical structure. The frequency of every “TMD” is tuned according to the mechanical structure requirement. The researcher name “the clerk” proposed the report about the concept of the “Multiple Tuned Mass Dampers (MTMDs)” and its optimization process. There is some research conducted by researchers about the usage of the “MTMD” along with the “doubly tuned mass damper (DTMD)”. In the case of the” harmonic excitation” and “zero-mean white-noise random excitation” the total efficiency of the “DTMD” is in the case of supporting the mechanical structure and reducing the vibration of the structure.

The research analysis shows the difference between the usages of the “DTMD” over a single mass ratio method “TMD”. The usage of the “DTMD” is more conventional than the “TMD” for all the range of the mass ratios. The recent research on the numerical and experimental analysis of the “TMD” is carried out for detecting the total efficiency of reducing the vibrations of the structure in the seismic response. In the year 1994, the three different models for analyzing the impact of the vibration on the mechanical structures are represented. The first is a 2D model which is about the shear building of two-story.

Next is a 3D model for the frame building of one story and the third model is also a 3d model of the bridge which is cable-stayed. This structural analysis is created using a total of 9 different earthquake records. The numerical analysis explains the response time of the “TMD” in different earthquakes for different structures is not the same for the same types of earthquakes. Some of the structure “TMD” responses were very efficient and but some structures are affected by the earthquakes so the “TMD” response is not effective. This analysis shows that different “TMD” in different structures' response times for reducing the vibration depends upon certain characteristics of the earthquake and the ground motion (Abdullah et al. 2021).

The response for reducing the vibration of the structure is huge in the case of resonant ground motions and diminishes when the main dominant frequency of the vibration goes further away from the mechanical structure. The effectiveness of the “TMD” is very limited for vibration-like seismic loading so to solve this problem the “MTMD” is installed in the structural construction for reducing the impact of the vibration. In the year of 1988, a new research paper is published related to the “multiple-tuned mass damper” which is able to reduce the impact of vibration on the building and mechanical structures.

This research methodology is based on the work of the researcher name “Den Hartog” and the research topic is based on the “single degree of freedom” and “multiple degrees of freedom”. In the year 1940, the simplified version of the “linear mathematical” models is represented by the statistical analysis of the “El Centro earthquake” and the response of the “TMD” is very useful for reducing the vibration of the earthquake and saving the building and the structures. Using parametric studies the development of increasing the performance of the tuned mass dampers under the induced wind condition and the performance of the both “passive and active tuned mass damper” can be done. From the few experimental and numerical analyses it can be stated that the “TMD” theory mainly consists of active control research and but using the parametric study the results of this experiment can be compared very well (Dai et al. 2021). The “TMD” has several constraints in the design but the usage of the “passive and active tuned mass damper” systems is necessary. So these two systems are installed in tall buildings and mechanical structures for reducing the dynamic impact of the induced wind and earthquakes.

In 1996 a research paper proposes the “passive vibration absorber” which is able to support tall and high-rise buildings and structural systems against the damages done by the earthquake. A new structure of “TDM” is prosed for the “one-mass” system and a “cantilever” system. The damping of the mechanical structure and vibration absorber is installed on the top of the structure. A new ground movement is designed by the actuator which is able to produce the vibration with different amplitude and frequencies. In 1996 another research paper is published about the implementation and usage of mass damper systems (Luo et al. 2019).

The mass damper system usage and its effects are clarified which is mainly about the many recorded values of the actual building against the induced wind vibrations and earthquakes. The discussion of this effect is based on the natural time period of buildings that are equipped with “mass damper systems”, “mass weight ratios to building weight”, and the “wind force levels” along with earthquake and the levels of ground motion. In 1997 a new method for the take an estimation of the parameters of tuned mass dampers in the case of seismic applications is developed.

In this research optimum parameters of the usage of the “TMD” in the building for reducing the impact of the vibration in the response of the mechanical structures to seismic loading of the design are mentioned in this research. The criterion that is taken into consideration for obtaining the optimum parameters is the mass ratio of the “TMD”, the frequency of the vibration, and damping ratios. These optimum parameters are used for calculating the several “single and multi-degree of freedom” of the big mechanical structures with installed “TMD” in different earthquake conditions. The results of the experiment show a significant reduction in the displacement and acceleration of the “TMD”s which are installed in the structures. Using this method of vibration control for mechanical sub-structures and configurations where these structures are used as vibration absorbers can be done. In the 1996 paper published about the “concise point of departure” for researchers who are wise to improve the current state and the design of the “DVA” and monitoring different structures made by civil engineers.

This theory helps to make links between structural control and many other fields like active and passive control of the structures and points out the similarities and dissimilarities along with its future research and application. In the year 2001, a research paper is published about the “Optimal placement of multiple tuned mass dampers” in the case of seismic structures. In this research, all the effects of the “tuned mass damper” and the modal responses against the earthquake for the Six-story building structure are studied and analyzed (Lang et al. 2020). The new form of tuned mass dampers like the multistage and multimode model is developed to make advances toward evolving the “DVA”. In this project design for the “DVA” is done using the software called “Ansys”. The effectiveness of the “TMD” is necessary for supporting the structures of the building (Bahrami et al. 2019).

The importance of the vibration absorber totally depends upon the mass ratio of the “TMD” and the frequency of the vibration. The design of the “DVA” must need to clarify that the structural failure because of the induced wind and the earthquake is inducing damage to the structure. In the year 2003 a research paper in publishes about the performance of the “DVA” in a five-story building and the benchmark model for the usage of the “active tuned mass damper” and a “fuzzy controller”. The research paper is about measuring the performance and efficiency of the “five-story benchmark model” by using the “active tuned mass damper (ATMD)” and the control over this action is achieved with the help of “Fuzzy logic controller (FLC)”.

The main advantages of the “Fuzzy controller” are the inherent “robustness” and the ability to handle all non-linear structural failure behavior. The usage of the “TMD” and both the active and passive control in structural failures is necessary. In 2004 another research paper is published explaining the induced Wind Response Control over the many mechanical structures with the help of Variable Stiffness in the “TMD”. In the year of 2006, an advanced research paper is published about the optimal analysis theory of the application of the usage of the TMD. In 2007, another research paper is published for supporting the “Optimum design and the structural analysis for the “passive tuned mass dampers” which are used in viscoelastic materials. In 2008 a research paper is published about the “Seismic Energy Dissipation of Inelastic Structures” with help of the “TMD” is discussed. To support this research another research paper is published about the “Dynamic analysis” of mechanical structures using the “multiple tuned mass dampers (MTD)”.

In the year of 2009 new research is developed for determining the efficiency and performance of a “nonlinear tuned mass damper (TMD)”. The latest research in the year 2010 is published on the topic of Vibration control for different seismic structures with the help of semi-active friction “multiple-tuned mass dampers (MTMD)”. This paper is about making a comparison of the system which uses the “passive friction-type multiple tuned mass dampers (PF-MTMDs)” and this ability to demonstrate the efficiency and the effectiveness of the “SAF-MTMD” which is able to suppress the seismic motion of a big mechanical structural system, and the visible to reduce the reducing the strokes of each and one mass unit, especially for high-scale earthquakes.

The methods discussed are the latest research related to developing the “dynamic vibration system’ for mechanical structures like bridges and aircftats, etc. the effectiveness and the efficiency and the performance of the “DVA”. This report is about discussing the new methods for the designing and optimizing the in the “Ansys” software. Using latest methods and technology the development of the “DVA” preceding rapidly to support the field of mechanical engineering.

2.3. Summary of research gaps in the existing work

Here, almost all of the research papers have considered the very basic design of the “DVA” in the form of a system pertaining to a spring mass (ASAMI et al. 2021). The reason for the aforementioned fact is the existence of a very simple framework which can verily be implemented without much expense. In this case, the suppression performance is limited to a certain extent which creates resonant frequencies that are to be averted. In most of the instances, the focus stayed on either “one” or “two” degrees of freedom in general while constructing the “DVA”. The drawback in this regard is the absence of proper study regarding the entire performance of “DVA” in respect of many degrees of freedom. The theoretical calculations have been done by way of the “un-damped” theory. But, these essentially require the presence of the factor of optimization in terms of the real world situations for being implemented in the definite use case in particular.

In the case of deducing a large set of vibration frequencies the development of numerous degrees of freedom “DVA” has to be in effect (Feudo et al. 2019). This in turn pertains to the enhancement of the total number of components present in the absorber along with its entire weight. The development of certain materials that have the capacity to absorb the vibrations over a range of frequencies can bring about a solution to the aforementioned issue. In the present situation, the polymer called “Sorbothane” is generally considered to act in the form of a best possible vibration absorber in respect of the issue in question.

A large quantity of the mass “spring damper” systems incorporate the material called stainless steel for the purpose of designing a vibration absorber. The point of concern here is that the aforementioned material is quite heavy as compared to the material aluminum. When it comes to the aircrafts, the width as well as the weight of stainless steel is to be brought down for optimal performance. Otherwise, it has the potential to enhance the factor known as “bucking”. Whereas, aluminum is lighter in weight as opposed to steel along with having an excellent capacity to absorb energy. This in turn refers to the aforementioned material to be the ideal one to absorb vibration. It also has the potential to bring down the “bucking” factor by dint of an increment in the material’s thickness.

The orientation of any absorber plays an important part in reducing the generated vibration. The absorber does not work efficiently when placed near the node of vibration in respect of the system in question (Ha et al. 2021). When it comes to the development of vibration absorbers for sophisticated systems, a set of suitable formulations are verily needed as far as the system is concerned. This in turn helps in evaluating the physical attributes of that vibration absorber.

2.4. Problem Definition

Fundamentally, the dynamic vibration absorber refers to a particular tool that helps to attenuate the generated noise as well as the structural vibrations. The underlying efficacy is contingent upon the reduction of structural vibrations at the narrow “band” level in particular. This also assists in bringing down the heavy vibrations along with greater levels of stability. The aforementioned factors are termed as being one of the primary reasons to incorporate vibration absorbers in the cabin of the airplane (Hua et al. 2018). VBA is essentially situated in relation to the target for that matter. The underlying working principles pertain to the reverberation produced by the main system, which in turn facilitates the absorber’s vibration. The ensued movement from the “DVA” produces the force of reaction which then gets disseminated to the main system. This thoroughly helps to control the main system’s vibration to a certain degree (Infante et al. 2018). In this case, the incorporation of supplementary “DVA” within the system in the form of a subsystem helps to boost the capacity of vibration control to a greater degree.

The inclusion of “DVA” in the cabin of the airplane mitigates the impact of noise ensued from the engine of the aircraft right up to the cabin area. This result is obtained with the help of low frequency and light weight “DVA”. In the case of the aircrafts there exists two categories of vibrations in general. One of these is the low frequency vibrations which are less than “20 Hz”. This kind of vibrations can be experienced by the whole of the body. The source of these vibrations is the existence of heavy components in the airplane, such as the horizontal stabilizer, elevator, and rudder, which are attached to the airplane’s frame. Another is the high frequency one, having a frequency greater than “25 Hz”. The hands and feet of the human body can experience the aforementioned frequency type. This vibration type comes from the small components present in the airplane, such as the door that is fixed on the aircraft’s frame. As the velocity of the airplane fluctuates and so do these vibrations.

The fundamental framework of the “DVA” consists of a number of components, such as quality, damping as well as stiffness. This absorber works as a subsystem attached to the vibration damper in the form of a target (Ji et al. 2022). Here, the ensued force of reaction brings down the level of vibration by way of resonance factor. An ideal vibration absorber is slated to contain a high “damping ratio” so as to suitably mitigate the vibrations.

On the basis of literature review a passive “DVA” equipped with a “mass spring damper” system is constructed for the purpose of fulfilling the desired objective. The aspects such as the design as well as analysis are predicted on the platforms of software called “Ansys”, and “Matlab” respectively. Here, “Aluminum Alloy 6061” is chosen to build the aforementioned system. This particular material has “2700 kg/m³ density, “310 MPa” tensile strength, and “250 MPa” tensile yield respectively. All of these attributes make this material suitable for any number of applications within the industry of aerospace. Here, Transient Analysis, Modal analysis, and statistical analysis have been taken into account for explaining the fundamental issue. Moreover, the simulation analysis is performed so as to validate the vibrations absorbers’ performance.

2.5 Data Analysis

Data analysis is crucial for c carrying out the implementation process in Ansys software. The software analysis has to be carried out for having the practical demonstration. The buildings or structure has to be designed in such a way that there could be minimum damage. The structure has to be analyzed in Ansys software so that all the insights could be understood to avoid any further structural damage. The structural damages could be avoided only if the reasons could be understood by the user. Ansys software has all the settings as well as features that could be further used for 3d modeling design as well as all the calculations. The calculation part has to be investigated to make sure there could be some prevention techniques. The prevention techniques could be used for preventing any structural failure. The interface has all the data that has to be provided one after the other for carrying out practical demonstrations. The instructions need to be carefully demonstrated for having a model design (Lang et al. 2020).

Basically, Ansys helps in carrying out FEA analysis. FEA analysis could be helpful in providing an accurate design. Many important issues like heat transfer, buckling analysis, and also thermal analysis. The objective is to design such a model that could prevent the damage caused by vibration. Any particular structure has to go through various types of loads. Earthquakes for decades have started causing damage to structures. The structures consist of parts that have to be designed so that any damage could be prevented. The structures like buildings, bridges and many more are designed by having reinforcement in it. Mechanical structures usually consist of concrete mix, as well as steel bars so that the building could be rigid as well as strong enough. Ansys software is there to help out civil engineers by carrying out FEA analysis.

3. METHODOLOGY

3.1. Introduction

The proper and accurate process is the main key to achieving success for any project and also for the organizations. Here in this project have to design and also optimizing a dynamic vibration absorber for a continuous mechanical design to reduce mechanical vibration. Here a structure is very important to construct a thing mechanically or physically and a mechanical structure which is everywhere and implemented in everything (ASAMI et al. 2021). Here the vibration excitations in mechanical structures like buildings, bridges, pipelines, and many others are produced by the natural cause and also for some human activity basically by the heavy machines used in the construction process. If the vibrational frequency is similar to the natural frequency then there occurs many problems and damages which was faced by the mechanical structures and the construction company and the projects are leads to failure. Here the dynamic vibration absorber absorbs the produced vibration and reduced the vibration frequency in the mechanical structure and decreased the damage rate of the constructal structure. Basically, the vibration absorber is used in the pipeline system project because the pipeline of a mechanical structure faces most of the vibration which is created by the turbulence of the water flow. The vibration absorber basically consists of a mass and an adjustable segment to decrease the vibration rate in the mechanical structures.

A dynamic vibration absorber basically disperses the produced vibration or energy and one of the most important things is for the vibration absorber to use or normalize the absorbed energy into the heat which stays in the viscous fluid. There are other ways to dissipate energy, for electromagnetic the absorbed vibration, can be stored in the form of heat and used later.

3.2. Research Approach

Essentially, the research approach is of three types which are known as Deductive approach for research, Abductive research approach, and Inductive approach of research. The deductive approach is contingent on the fact of developing a particular hypothesis or a set of hypotheses that are predicted on an existing theory. In this approach, the factor of reasoning moves from particular to general on the whole (Luo et al. 2019). The abductive research approach aims to address all the weaknesses linked with the rest of the research approaches. In this kind of approach, the process of the research begins with “puzzles”, or “surprising facts”. The aforementioned factors emerge at that time when the concerned researchers come across an “empirical” phenomenon which cannot be elucidated with the help of the existing theories.

In the case of the inductive approach of research, the process begins with the theories as well as the observations which are brought about at the end of the “research process”. This approach aims for the abstraction of patterns from the observations. The development of the explanations and theories takes place in respect of these patterns with the help of a set of hypotheses in general. In the present context of the research, the Deductive Approach has been taken into consideration.

3.3. Research Design

The term research design pertains to the basic framework of the research methods as well as the techniques selected by the concerned researchers in order to conduct the whole of the study. It permits the researcher to suitably sharpen all of the research methods suitable for the core of the research topic. The type of research design is very crucial with respect to the aspect of selecting the best model for the study in question. The design of research has been classified in two sections, which are Qualitative design of research, and Quantitative design of research respectively.

Quantitative Design

This kind of research design helps to determine the underlying relationship amongst the gathered data along with the observations predicated on the mathematical calculations (Noori et al. 2019). The statistical methods can easily disprove or prove the theories linked to any natural occurring phenomenon. It also assists in determining “why” any specific theory is in existence along with “what” all the respondents have to conclude about it.

In this specific research, the Qualitative Design has been considered to perform the corresponding tasks.

Qualitative Design

This type of research design is applicable for such cases wherein the statistical conclusions for collecting the “actionable insights” are crucial. Here, the numbers render a better perspective in order to make critical “business decisions”.

3.4. Develop a dynamic vibration absorber in ANSYS and perform Statistical Energy Analysis (SEA)

An impenetrable system of acoustic and structure most likely to be sketched as a mixture of N subsystems relies on conditions of their connections. The coupling loss factor and energy loss are the key features that determine the energy transmissions among the subsystems. In this case, subsystem the energy equations of can be written as represented by equation Error: Reference source not found)

(1)

Where,

P - Input power, – Energy loss factor, w – Coupling loss factor

The aircraft composite panel that we have considered here is a double-wall like structure and it is subdivided into five different substructures as shown in Figure 2.

Figure 2: Substructures Block-diagram of aircraft Composite Panels

The energy equation defining the impound surveillance to airborne excitation can be represented by equation Error: Reference source not found),

= (2)

We are able to estimate the transmission loss by equation Error: Reference source not found),

(3)

Where, S is the panel Area

3.5. Determination of SEA Parameters by indirect Coupling Method

The evaluation of SEA parameters can be done using different approaches but the most suitable approach for weak coupled structures is the loss factor of indirect coupling theory of traditional SEA as it would result in more efficient results.

The indirect coupling factors can be derived from equations (Error: Reference source not found) and Error: Reference source not found) for N number of substructures that are coupled in series array,

(4)

(5)

These equations indicate that if the coupling of the substructures is weak, there might be negligible loss factor whereas for a strong coupling it would be of significant indirect coupling.

3.6. Simulation Setup in ANSYS

The composite panel from an actual aircraft composite panel of dimension 1.42mx1.58 m and 0.8 mm thick is shown in Figure 3. The double wall structure was constructed using a 0.4mm thick aluminium panel. The testing panel is installed between a vibration area and a non-resonant bower as shown in Figure 3. The vibration area was of volumetric dimensions of 5.60m x 4.30m x 3.75m and that of non-resonant bower of 4.40m x 4.60m x 3.10m. Sources for generating vibrations were placed in the vibration area and the non-resonant bower in the receiving space.

Figure 3

1. c The Composite panel. 3. c Installation of panel3. c Stringer cross-section

The procedure for loss of transmission test is archetypal. The natural frequencies and vibration modes were obtained by the modal analysis test and results would be tabulated. These tested data would eventually be used for the comparative evaluation. Figure 4 shows the designed dynamic vibration absorbers which are viable to be tuned at the desired frequency. The fuselage is riveted with the absorber parallel to the panel. The mass spring damper system as shown in Figure 4 is simulated in ANSYS with two degrees of freedom.

Figure 4: Designed Absorber

3.7. Experimental setup and design

Here in the process of making a dynamic vibration absorber, an experiment is very necessary for the mechanical structure. Basically, an experimental model has four parts which are the mechanical structure, unbalanced weighted motor, vibrometer, and beam DVA. Here produce a practical arrangement of the mechanical structure which is similar to the actual project or the constructional structure to test the vibration absorber functionality. Here the geometric and physical properties of the mechanical structure are used in the experimental model to execute the theoretical and the practical test for the structural safety concern. Therefore the unbalanced weighted motor is used in the mechanical structure to produce the excitations. This motor is connected to a frequency drive where it can give the desired frequency for the mechanical structures. It can be increasing and also decrease as per the testing requirements where the absorber can test it practically. Next, the vibrometer is here in the absorber monitoring the frequency which has a specific range between 2 to 10000Hz and it is also able to measure the acceleration, velocity, and displacement in the mechanical structure. In the end, the beam DVA is a model which contains an L-shaped beam to absorb the kinetic energy both horizontally and vertically. It is mostly used in beam construction projects where threaded rods are used to construct the beam (Love et al. 2021).

This beam structure experimental setup is basically an effective test bed for the vibration absorber and it is also used in many engineering fields.

The following research is the basis of a vibration-absorbing system dynamically. The resources to collect the datasets from various resources like journals and articles can be observed to further utilize the concept (Lang et al. 2022). This is a mechanical implementation on the bases of several application-based vehicles or large kinds of buildings for the purpose of absorbing vibration. There are many purposes of the vibration that can occur on the bases of different scenarios, so every perspective of the bases of vibration occurring has to be observed. There are many such vibration isolation techniques that have to be observed and it can be stated in different dimensional stages so every aspect has to learn the perspective. There the purposes of preventing vibrational isolation, the parametric design to the reflective optimization, “Ansys '' are generated three-dimensional model based designing for the purpose of finite kind of element base analysis. There are several design modelers that can be used to design their purpose in terms of vibrational isolation (Venczel et al. 2020). The purpose of controlling motion in the structure-based mechanism and the application based on the different frequencies of the framework to neutralize the vibration is to observe by collecting the database to find the total phenomena of the modelling.

The represented analytics purposes various experimental designing can be taken to observe the different perspectives (ZHANG et al. 2021). There are several geometrical approaches that can be taken to implement the configured model, the geometrical approaches can be specified in the bases of the piston, spring, or the other connective property, and the structural materials are figurized in the coordinate-wise functionality, and the many several contracts regions to resist the vibrational effect, the purpose of the said functionality bases the actual modelling can be done in design analytic languages. There are several thermal conduciveness can be observed graphically in the purpose of pressure (Zhou & Hou, 2020). The structural methodology can be specified in many aspects like the isotropic elasticity of the structural steel in various ratios or modulus beneficiary, it can be derived from “Bulk Modules” or the basses of “Poisson’s Ratio”, the comprehensive straightness of the structural methodology can be observed in much geometrical structure. The analysis can be processed in various harmonic response analyses, for the purpose of rotating the speed in three purposes of frequency. The effectiveness of several heat-transmitting properties, the particular representation is basically done to the simulation purposes in the system without any presence of vibrational isolation.

The finite element-based structural model is testing the natural frequency in terms of various curve filtering to transfer the structural execution in a decorated way. There is various kind of module-based operators to figure out the row and column-based executing properties. The finite-based element methods are implemented in various dipole-based modification, dipole is basically structured in silicon kind of steel-based modification to compose the mechanism functionalities. The many natural bases generating frequency can be observed throughout the mechanism purposes. The total structural modification can be performed in the x-y or z axes of the dipole configuration. The sensing of the acceleration management is organizing the testing properties in a sequential scenario. The ratio based on frequency generation can be modified in various adat processing procedures. The increment or the decrease in many occurrences can occur for the purpose of various graphical plots. The stimulation process can be done of the modification dynamically by the software-based designing language “Ansys”. The result collected from the dynamic analysis can be structured in a many-spectrum analysis.

3.8. Technical Aspects

A vibration or shock is common for a mechanical structure which is basically produced from the kinetic energy and caused several damages to the mechanical structure and the construction. Mechanical damage in the mechanical system can generate faults and also damage the manufacturing and processing components of the mechanical structure. Vibration attenuation features can be contained in shock absorbers, linear dampers, spring isolators, elastomeric isolators, air springs, or some mechanical damping treatments which helps the producers reduce equipment rest and cost limitations. This system can be used in a wide range of applications, from the construction field to the automobile mechanism and thereafter

In the field of farming, aircraft, GPS system, and many more where heavy equipment is used, vibration absorber systems are used to reduce mechanical and also natural vibration. Here most vibration absorbers conduct their damping aspects using hydraulic fluids which are forced by a piston and rod via small holes to produce damping, and therefore a compressed gas drove out from it (Auleley et al. 2021). This gas generates a spring pressure to push back the rod to its starting place when the pressure is released. Basically, the vibration absorbers are formed by high-strength steel to endure the pressure and save the mechanical structure from damage.

In the present day, the developer tries to construct an absorption system with longer service life and compact structure. Noise reduction techniques are now also added to the dynamic vibration absorber system to make the absorber more suitable and acceptable. A specific application for the vibration absorber devices has come with the improved awareness for environmental protection of our infrastructures like buildings, bridges, and many more. By adding damping to these structures, energy is absorbed by the hydraulic machines without damaging the mechanical structure.

An isolator is a very important thing for the vibration absorber and it is made from very high-strength materials like carbon steel, stainless steel, and others. Elastomeric isolator basically contains metallic components which provide the stiffness and proper damping for the vibration absorber. Most of the vibration absorber design is reusable and also self-contained which offers a lot of advantages and disadvantages to the mechanical structures.

Advantage

There is a lot of advantage to using a vibration absorber for a mechanical structure where it reduces the damage and failure rate. A vibration absorber particularly reduces vibration on machinery which reduces internal damage, maintenance costs, and downtime. Here absorber also increased the production rate and also provide a higher and smoothed momentum to the mechanical structure removing the moving object. An unnatural noise, vibrations, or damaging impact is very harmful to a mechanical structure and affects the product quality. Here the vibration absorber eliminated those motions which increased the product quality for mechanical machinery (TOMIOKA et al. 2021).

Simply saying a vibration absorber system provides longer lives, lower maintenance, and safe operations to the mechanical structure or the infrastructure.

Disadvantage

Being an important part of the mechanical structure there are some disadvantages to using the vibration absorber system. In the absorber when the forcing frequency is similar to the natural frequency of the central mass the comeback is infinite, which is called resonance, which is cause some problems for vibrating structures. The dynamic vibration absorber is performed only at a specific frequency that fits its resonant mode which is a major disadvantage for the vibration absorber. Here it is complicated to calculate numerically and also shows some problems when it applies to a nonlinear system. In the dynamic vibration absorber, PRV sometimes misleads the results and gives some errors.

3.9. ANSYS Simulation

Mass damping for a vibration absorber is manufactured in the ANSYS domain and the system. A damper is basically constructed by a mass block and a spring system for the compile the test. Here basically used some high-strength materials to develop the system because of its specific characteristics. Stainless steel, carbon steel, aluminum, and others are the main materials for developing the system because these materials are very good in energy consumption which is very important for the vibration absorption process (Qin et al. 2021).

1. Mesh analysis in ANSYS

Mesh analysis is the process of constructing 2D and 3D grids which simplifies the process of dividing the critical geometries to discretize a field. The mesh analysis in ANSYS makes progressive automatic mesh generation tools that can deliver faster and more accurate solutions for CFD which is a type of fluid and also FEA Meshing.

1. Model analysis in ANSYS

The model analysis is a basic dynamic study type that provides some natural frequency to the mechanical structure for resonating. This natural frequency is very important in the field of structural engineering because with the help of the natural frequency of the mechanical structure the engineers can differentiate it from the seismic waves or the fre4quency which was created by earthquakes and other natural disasters.

1. Harmonic analysis in ANSYS

In the construction field, the overload of the materials on the structures is very important for a vibration absorber. Here the ANSYS and the mechanical workbench can conduct a base acceleration in harmonic analysis on the mechanical structures. Basically, with the help of harmonic analysis, the response of the structure to the excessive load gives the proper solution to the infrastructure.

1. Transient analysis in ANSYS

Transient analysis is the process of measuring and defining the impacts of the loads and internal forces that are a process of time on a mechanical structure. Basically, it is used to specify the dynamic response of a mechanical structure under the movement of any time-dependent loads. Transient analysis generally depends on the DOFs involvement and is also solved by the appropriate procedure (Trujillo-Franco et al. 2022).

1. Static analysis in ANSYS

A static structural analysis computes the effect of continuous loading conditions on a structure while ignoring inactivity and damping effects, such as those generated by time-varying loads. Here a static analysis also defines the displacement, stresses, strains, and forces in the mechanical structure which is basically generated by the loads.

3.10. Process and steps involved in the design process adopted

The processing is the reflective implementation for the purpose of software analysis. The practical demonstration is constructed throughout the software analysis. There the implementation of the process can be done by the “Ansys” software, the purpose that, the building structure has to practically demonstrate that can resolve the damaging purposes (Ding & J, 2019). The structural damage can be minimized by setting the feature weise configuration for the purposes of 3d kind of modeling design in a technical representation to prevent the damage. Basically, the following configuration can be performed in various feature base element analyses for designing purposes. There are many other aspects like transferring the heat for the purposes of heat transferring methodological thermal analysis. There are many other perspectives that can be analyzed like buckling analysis to the bases of designing the vibrational resistance modeling processes (Tao).

The purposes of building construction the earthquake has impactful issues to damaging the structure, basic structure of the construction like several long bridges, and very large buildings, there mainly steel-based mixed construction phenomena is represented, so the represented analysis in the “Ansys” is reflecting the engineers to implementing feature wise element analysis called “FEA” to help the structural mechanism to resist the vibrational isolation. There are many functional analyses that can be done for the purpose of the mechanism of the modelling. The magnetostrictive approaches can be done through our designing purpose, the represented model is ambler to implement the resist the vibrational isolation effectively, and the controlling of the mechanical or thermal field has to be coupled dynamically to the purpose of transmitting the frequency dynamically (Luo et al. 2019 ). There are some vibrational problems that can occur in the cases of some overloaded vehicles or dumpers there is the high frequency of the vibrational force can be occurred so this kind of software-based analytics model can be applied for that purpose to resist the vibration.

Chapter 4: Results and analysis

4.1. Introduction

The represented analysis of optimizing the vibration resistance design, there are a rapid number of cycling synchronization that can be done, there are many topological folded models are reflected the management purpose, and there are many sets of dipole magnetic field orientation to accelerating the technical indexes to reduce the vibration, there are several factors can be observed to modeling the functionality. The common thing here for the objective purpose is to analyze the testing fundamentals in the bases of linear vibrations;l forms. The model of designing is mainly based on the finite element method to reflect the relative excitation in the bases of vibration that occurred. There are many factors that are performed to analyze the damping ratio on the bases of vibrational methodology to a dynamical characteristic to provide the vibration-free mechanism.

4.2. Implementation

The implementation of the represented vibration resistance optimization, “Ansys' ' are used to provide the simulation in multibody dynamical approaches. The “Ansys' ' is basically processing the electromagnetic noises in the perspective of the vibration; it can be structured as several graphical representations for the purposes of curve lines or line-based parameters. The geometrical approaches can be performed on the bases of connecting nodes, several piston analyses, and supportive objectives in the reflected coordinate system globally. The contact region can be analyzed in the bases of regional; analysis of the contract region of the bodies. The analysis of it can give the visualization of the contract body and the targeted body preferences. The analysis purpose occurred in the particle-wise analysis methodology in a structured way.

The analysis settings can visualize the static information to the providation og the solutional information. The several co ordinate wise visualization are can be done in the particular analyzing visualization. There are many structural analyses that can be performed to optimize the models. The structural analysis can be done for the purpose of density or the preferable isotropic elasticity of the particulars. There are many modulus derivations can be performed to measure the objective in a geometric plot. The thermal expansion can be implemented to figure out the ultimate strength ness in showcasing the line parameters.

The spring of the preferable representation can be used to utilize the particular aspect to provide the objectives of the vibration and required methodology to analyze vibration-free designing provision. The static analysis can be done in various aspects like the analysis of the settings of the particular particle on the bases of force-generating factors and the fixed support objectives. The solution of the vibrational purpose can be performed in dynamic analytics away from the abuses of formation analysis.

The equivalent strain can be observed elastically, and the strain energy should be measured to figure out the output. The represented model basically analyzes the finding elements to the various applications based on the dumper kind of overloaded vehicles to overcome the jerking purposes or like the large building to provide the vibrational free in the bases of occurring earthquakes the implementation of the model is beneficial to approach. There are many motion-based rotations ot\r the frequency generation properties that can be observed throughout the analysis for the purposes of occurring on the bases of the vibrational isolation. The structural mechanism can be displayed in the three-dimensional approaches to neutralize the vibrational occurrence in the structural purposes mechanism of the buildings or the overloaded dumper kinds of vehicles, the application of it is able to provide the vibration-free output modeling purposes.

4.3. Result and implementation

Figure 4.1: Structural Steel Characteristics

(Acquired from Ansys)

The picture attached above showcases a number of attributes that are linked to the structural steel in particular. The “strain-life parameters” and the “S-N Curve” are displayed in this section (Cirelli et al. 2019). Here, the values of “Tensile Ultimate Strength”, and “Tensile Yield Strength” are “4.6e⁺⁰⁸ Pa”, and “2.5e⁺⁰⁸ Pa” respectively. In case of the thermal properties, the parameters such as “Isotropic Thermal Conductivity”, and “Specific Heat Constant Pressure” are also shown. The values of the aforementioned parameters are “60.5 W/m-°C”, and 434 J/kg °C” respectively.

Figure 4.2: Contact Region and Analysis for Piston

(Collected from Ansys)

In this image the connections have been made that are further displayed in the “Ansys” software platform. All of the contact regions have been connected with one another to form the entire shape of this element (Fernandez Escudero, 2021). The contact region in color “red” refers to the “Contact Bodies”, and the “blue” one refers to the “Target Bodies” respectively.

Figure 4.3: Analysis for spring

(Retrieved from Ansys)

The figure and the parameters displayed in the above image refers to the aspect of geometric modeling and analysis in respect of the element “Spring”. The material which has been taken up for performing the model analysis is “Structural Steel” in this regard (Fuqing et al. 2022). The contact regions are connected in order to form the entire connection between all the individual layers.

Figure 4.4: Geometric Analysis of Piston

(Obtained from Ansys)

According to the above figure, a piston has been represented and the piston has seven contact regions. The contact regions depict the portions of the piston where external contact is experienced. Due to contact with external objects, the piston experiences an interaction with forces and the target body view of the piston has been shown alongside the piston. The figure represents Geometrical analysis of the piston that has been drawn using the software tool Ansys.

Figure 4.5: Finite Element Analysis and Mesh Analysis

(Collected from Ansys)

This particular image has been obtained after performing the finite element analysis. It is nothing but a particular process for simulating the overall behavior of a specific part or a whole assembly under the provided conditions (Javanshir et al. 2021). This in turn helps in simulating the required physical phenomena which reduces the requirement for the physical prototypes. The optimisation of all of the included components are also enabled in this regard as an element of the “design” process. Essentially, “FEA” utilizes the mathematical models for the purpose of comprehending and quantifying all the effects of the real-world conditions in respect of a part or an assembly.

All of these simulations that have been performed by way of the software platform “Ansys” help to locate all the potential issues within a particular design. This includes the weak spots as well as the tension areas respectively. The above element has been cut into a number of pieces and then joined together in the aforementioned software platform, at specific points known as nodes.

Moreover, the Mesh Analysis refers to the process of turning all of the irregular shapes into more understandable volumes, that are known by the name “elements” in this case (Kolyshev et al. 2019). It generally assists in bringing down the total quantity of effort and time spent in order to attain the results in an accurate manner.

Figure 4.6: Geometry of the Spring

(Retrieved from Ansys)

The material in this image is one of the many parts that has constituted the entire process of model analysis in respect of their geometric configuration (Li, 2021). All the contact regions along with corresponding connections are also displayed in this regard.

Figure 4.7: Analysis of Spring

(Obtained from Ansys)

The element in this picture above is a “spring” that has been a part of the geometric model analysis amongst other materials. The “7” regions of contact have also been displayed, by taking the assistance from “Ansys” software platform, that helps in forming the overall connection.

Figure 4.8: Parameters of Structural Steel

(Collected from Ansys)

The picture showcases a lot of crucial parameters that together describe the properties of the element in question. The density in this case is “7850 kg/m³”. The properties related to the isotropic elasticity of the concerned material has also been obtained with the help of the “Ansys” software platform (Lisitano, 2021). The values regarding some of the obtained parameters such as Bulk Modulus, Shear Modulus, Poisson’s Ratio are “1.667e⁺¹¹ Pa”, “7.6923e⁺¹⁰ Pa”, and “0.3” respectively.

Figure 4.9: Outcome of Solution

(Obtained from Ansys)

A spring has been depicted in the above figure and this spring has been used for geometric model analysis. The figure has been formed with the help of the software platform called Ansys. The strain energy of the spring has been studied for this assignment and the strain is the force which is exerted by the spring as a reaction to the load on the spring (Özyar, 2021). The different forces experienced by the spring consists of the equivalent elastic strain, Equivalent stress, and the strain energy generated from the spring. The spring has been created to scale using the software tool Ansys and the spring has been constructed using reliable material.

Figure 4.10: Solution Results

(Acquired from Ansys)

According to the above figure a spring has been depicted and it has been created using the software platform called Ansys. The spring is a part of the solution results that has been created using the software tool called Ansys (Pappalardo et al. 2018). The spring has been drawn to scale and the spring can be exerted to different forces which can be categorized into stress and strain. Load can be attached to the spring and the spring can feel strain forces due to the force exerted by the load. The spring has been constructed using reliable materials.

Figure 4.11: Solution Outcomes

(Collected from Ansys)

In the above figure, the solution outcomes created using the software tool called Ansys has been depicted. In the figure, a spring has been represented and the spring has been drawn to scale. The spring is subject to stress and strain and the spring is made of reliable material.

5. Conclusion & Future Recommendations

5.1. Conclusion

High degree of noise is very common when it comes to the interior of the aircrafts. This in turn brings about certain issues for the crews and the passengers, such as discomfort issues, speech interference etc. The comprehensive usage of the dynamic vibration absorber has proven to be of great value for the purpose of mitigating the noise levels in the aircraft’s interior. In case of material selection, aluminium has been prioritized over stainless steel so as to avoid a number of impediments regarding the aircraft. The ideal material has been a polymer called “Sorbothane” in this regard. Many degrees of freedom have been taken into consideration while implementing the damping vibration absorber. The frequency types are also taken into account as far as the functions of “DVA” are concerned.

5.2. Linking with Objectives

Linking with objective 1

A suitable model of a spring-mass damping vibration absorber is constructed inside “Ansys” Design Modeller.

Linking with objective 2

The overall performance level of the “DVA” is carefully evaluated by way of “Finite Element Analysis” within the software platform Ansys.

Linking with objective 3

A “three-dimensional” couple dynamic system is constructed with respect to the aspect of vibrational analysis through the Ansys “parametric” design language.

Linking with objective 4

The “vibration isolation” performance of the damping vibration absorber is determined while the dynamic and harmonic conditions of “loading” are in effect.

5.3. Recommendations

The benefits of “DVA” have been explained in the earlier sections (Pokhrel et al. 2020). Although the inconsistencies of the system in question have been elucidated, there also remains some crucial insights which need to be taken care of while using this system. The advantage of this system lies in its ability to reduce the vibration levels over a large range of frequencies. The area where this device is getting placed has to be considered with utmost importance as a lesser distance from the source of vibration can yield better performance in terms of the observed output. Here, only two degrees of freedom have been taken into consideration with respect to the damping vibration absorber system (Raze, 2021). But, in the ideal condition the system has to operate across multiple degrees of freedom in general.

5.4. Future Scope

Here, the use of aluminium has been specified as opposed to the use of stainless steel. As the former has better characteristics in respect of the required necessities, such as light weight, etc, it has been opted in this context (Tian et al. 2021). This material has the ability to bring down the factor called “bucking” by dint of having more thickness for that matter. But, for this system to showcase optimum results the polymer called “sorbothane” has to be used in almost all of the occasions. The sole reason for the aforementioned case is this material’s better performance in terms of the desired parameters which is light weight amongst others. This in turn helps in bringing down the energy level in the most efficient manner possible (Tishhenko et al. 2020). When it comes to the aircrafts, this system has to be mounted at the right place in relation to the airframe, so that most of the energy is absorbed without using up much of the resources.

5.5. Limitations

Here, there exists some key factors that have restricted the entire performance of the system up to a certain extent. The first one being the “suppression performance” that has been restricted to a specific limit. This in turn generates “resonant frequencies” within the system which need to be discarded in order for the system to perform in its optimum capacity (Xiao et al. 2019). The consideration of only “one” and “two” degrees of freedom are also an impediment in this case as far as the construction of a damping vibration absorber is concerned.

In reality, the existence of “multiple” degrees of freedom essentially enhances the underlying performance pertaining to the “DVA”. The inclusion of “un-damped” theory in terms of the calculation aspect has not been very convenient in this regard. Fundamentally, it needs the existence of an “optimization factor” for the purpose of addressing the real-world issue in general. The existence of “multiple” degrees of freedom generally increases the total quantity of elements existing inside of the absorber, resulting in a greater material weight. The solution with regards to the aforementioned issue is the incrpairing of pertinent material into the system that has been discussed earlier.

5.6. Summary

In this research project, the earlier mentioned software platforms have been for the sole purpose of constructing the design model of the “spring-mass” damping vibration absorber in particular. The efficiency in its performance has also been assessed through “Finite Element Analysis”. The loading conditions such as “harmonic”, and “dynamic” have been in force, in which the “vibration isolation” performance of the “DVA” has been decided.

The aspect of choosing the right material holds much significance in this case, because only the pertinent material can show the best outcome when it comes to the absorption of vibration. The inclusion of stainless steel has brought about a number of hindrances that have contributed to the overall performance of the “DVA”. The high amount of weight pertaining to the aforementioned material has increased the “bucking” factor. Whereas, the incorporation of aluminium has by far mitigated the vibration level by dint of having lesser weight than that of stainless steel. Aluminium also has an excellent ability to address the factor called “bucking”, as it has greater thickness. Another critical aspect is the “orientation” factor, which in turn facilitates the efficacy of the “DVA” in absorbing all of the vibrations.

References

• Rossato, B. B. and Miguel, L. F. (2021). Robust optimum design of tuned mass dampers for high-rise buildings subject to wind-induced vibration. Numerical Algebra, Control and Optimization, 2155-3289. doi:doi:10.3934/naco.2021060
• Rincón, C., Alencastre, J. and Rive, R. (2021). Active Vibration Absorber for a Continuous Structure Model. doi:10.31224/osf.io/r3ujn
• Wang, X., Liu, X., Shan, Y., Shen, Y. and He, T. (2018). Analysis and Optimization of the Novel Inerter-Based Dynamic Vibration Absorbers. IEEE Access, 6, 33169-33182. doi:10.1109/ACCESS.2018.2844086
• Lavazec, D., Cumunel, G., Duhamel, D. and Soize, C. (2017). Attenuation of acoustic waves and mechanical vibrations at low frequencies by a nonlinear dynamical absorber. Congrès Français de Mécanique (CFM 2017) (pp. 1-12). Lille: hal-01585746. Retrieved from https://hal-upec-upem.archives-ouvertes.fr/hal-01585746
• Kari, L. (2020). Are Single Polymer Network Hydrogels with Chemical and Physical Cross-Links a Promising Dynamic Vibration Absorber Material? A Simulation Model Inquiry. Materials, 13(5127), 1-19. doi:10.3390/ma13225127
• Richiedei, D., Tamellin, I. and Trevisani, A. (2022). Beyond the Tuned Mass Damper: a Comparative Study of Passive Approaches to Vibration Absorption Through Antiresonance Assignment. Archives of Computational Methods in Engineering,29, 519-544. doi:10.1007/s11831-021-09583-w
• Zhou, S., Mistral, C. J. and Chesne, S. (2019). Closed-form solutions to optimal parameters of dynamic vibration absorbers with negative stiffness under harmonic and transient excitation. International Journal of Mechanical Sciences, 157-158, 528-541. doi:10.1016/j.ijmecsci.2019.05.005
• Sayyed, A. B., Sonar, G., Suryawanshi, K., Shaikh, M. G. and Taware, S. (2020). Design and Analysis of Tune Mass Damper System. International Journal of Engineering Research & Technology (IJERT), 9(10), 588-591.
• Özer, A., Ghodsi, M., Sekiguchi, A., Saleem, A. and Al-Sabari, M. N. (2015). Design and Experimental Implementation of a Beam-Type Twin Dynamic Vibration Absorber for a Cantilevered Flexible Structure Carrying an Unbalanced Rotor: Numerical and Experimental Observations. Shock and Vibration, 2015, 1-9. doi:10.1155/2015/154892
• Chai, C. S. and Ko, Y. H. (2021). Design and Experimental Implementation of a Passive Dynamic Vibration Absorber to Attenuate Broadband Vibration. Journal of Physics: Conference Series, 2051, 1-7. doi:10.1088/1742-6596/2051/1/012020
• Sriramdas, R., Rastogi, S. and Pratap, R. (2016). Design Considerations for Optimal Absorption of Energy from a Vibration Source by an Array of Harvesters. Energy Harvesting and Systems, 3(2), 121–131. doi:10.1515/ehs-2015-0021
• Teik, H. S. (2013). DESIGN OF A DYNAMIC VIBRATION ABSORBER. Melaka: Universiti Teknikal Malaysia.
• Harik, R. F. and Issa, J. S. (2013). Design of a vibration absorber for harmonically forced damped systems. Journal of Vibration and Control, 0(0), 1-11. doi:10.1177/1077546313501928
• Luan, S., Arora, M., Thurston, D. L. and Allison, J. T. (2017). DEVELOPING AND COMPARING ALTERNATIVE DESIGN OPTIMIZATION FORMULATIONS FOR A VIBRATION ABSORBER EXAMPLE. ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (pp. 1-12). Cleveland: IDETC/CIE 2017.
• Yoon, G. H., Choi, H. and So, H. (2021). Development and optimization of a resonance-based mechanical dynamic absorber structure for multiple frequencies. Journal of Low Frequency Noise, 40(2), 880-897. doi:10.1177/1461348419855533
• Singh, A. P., Sharma, D., Chouhan, J., Shankhwar, K., Thakur, K., Javre, P. and Pande, V. (2012). DYNAMIC VIBRATION ABSORBER. Bhopal: Rajiv Gandhi Proudyogiki Vishwavidyalaya.
• Desen, I. C. (2000). EXPERIMENTAL STUDY ON AN IMPACT VIBRATION ABSORBER. Texas: Texas Tech University.
• Harel, S. S. (2017). FREQUENCY TUNING OF VIBRATION ABSORBER USING TOPOLOGY OPTIMIZATION. Arlington: The University of Texas at Arlington.
• Monkova, K., Vasina, M., Zaludek, M., Monka, P. P. and Tkac, J. (2021). Mechanical Vibration Damping and Compression Properties of a Lattice Structure. Materials, 14(1502), 1-16. doi:10.3390/ma14061502
• Broch, J. T. (1984). Mechanical Vibration and Shock Measurements. NÆRUM: K. LARSEN & SON A/S.
• Naucler, P. (2005). Modeling and Control of Vibration. Uppsala: UPPSALA UNIVERSITY.
• Taflanidis, A. A., Giaralis, A. and Patsialis, D. (2019). Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures. Journal of The Franklin Institute, 1-36. doi:10.1016/j.jfranklin.2019.02.022
• Carbajal, F. B., Badillo, H. Y., Olvera, R. T., Contreras, A. F., Gonzalez, A. V. and Garcia, I. L. (2022). On Active Vibration Absorption in Motion Control of a Quadrotor UAV. Mathematics, 10(235), 1-25. doi:10.3390/math10020235
• Hua, Y., Wong, W. and Cheng, L. (2018). Optimal design of a beam-based dynamic vibration absorber using fixed-points theory. Journal of Sound and Vibration, 421, 111-131. doi:10.1016/j.jsv.2018.01.058
• Li, Y., Lombardi, L., Luca, F. D., Farbiarz, Y., Blandon, J. J., Lara, L. A., . . . Neild, S. (2019). Optimal design of inerter-integrated vibration absorbers for seismic retrofitting of a high-rise building in Colombia. Journal of Physics: Conference Series, 1264, 1-12. doi:10.1088/1742-6596/1264/1/012031
• Piccirillo, V., Tusseta, A. M. and Balthazara, J. M. (2019). OPTIMIZATION OF DYNAMIC VIBRATION ABSORBERS BASED ON EQUAL-PEAK THEORY. Latin American Journal of Solids and Structures, 16(4), 1-22. doi:10.1590/1679-78255285
• Rade, D. A. and Steffen, V. J. (2000). OPTIMISATION OF DYNAMIC VIBRATION ABSORBERS OVER A FREQUENCY BAND. Mechanical Systems and Signal Processing, 14(5), 679-690. doi:10.1006/mssp.2000.1319
• Diveyev, B., Hlobchak, M., Martyn, V. and Yavorskyy, Y. (2015). OPTIMIZATION OF IMPACT DYNAMIC VIBRATION. Lviv: Lviv National Polytechnic University.
• ARAZ, O. and KAHYA, V. (2021). OPTIMIZATION OF NON-TRADITIONAL TUNED MASS DAMPER FOR DAMPED STRUCTURES UNDER HARMONIC EXCITATION. Bursa Uluda? University Journal of The Faculty of Engineering, 26(3), 1021-1034. doi:10.17482/uumfd.878114
• Zhu, X., Chen, Z. and Jiao, Y. (2018). Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates. Journal of Low Frequency Noise, 37(4), 1188-1200. doi:10.1177/1461348418794563
• Saadabad, N. A., Moradi, H. and Vossoughi, G. R. (2019). Optimized design of adaptable vibrations suppressors in semi-active control of circular plate vibrations. Scientia Iranica Transactions B: Mechanical Engineering, 26(3), 1358{1377. doi:10.24200/sci.2018.20417
• Pachpute, A. Z. and Bawa, P. B. (2016). Optimum Design of Damped Dynamic Vibration Absorber – A Simulation Approach. International Journal of Recent Engineering Research and Development (IJRERD), 01(02), 19-21.
• Mayer, D. and Herold, S. (2018). Passive, Adaptive, Active Vibration Control, and Integrated Approaches. IntechOpen. doi:10.5772/intechopen.71838
• Krenk, S. (2019). Resonant inerter based vibration absorbers on flexible structures. Journal of the Franklin Institute, 356, 1-30. doi:10.1016/j.jfranklin.2018.11.038
• Pani, S., Senapati, S. K., Patra, K. C. and Nath, P. (2017). Review of an Effective Dynamic Vibration Absorber for a Simply Supported Beam and Parametric Optimization to Reduce Vibration Amplitude. International Journal of Engineering Research and Application, 7(7), 49-77. doi:10.9790/9622-0707034977
• Au-Yeung, K. Y., Yang, B., Sun, L. and Ba, K. (2019). Super Damping of Mechanical Vibrations. Scientific Reports nature research, 9, 1-10. doi:10.1038/s41598-019-54343-3
• Dogan, H., Sims, N. D. and Wagg, D. J. (2020). THE EFFECTS OF PARASITIC MASS ON THE PERFORMANCE OF INERTER-BASED DYNAMIC VIBRATION ABSORBERS. In M. Papadrakakis, M. Fragiadakis, & C. Papadimitriou (Ed.), EURODYN 2020: Proceedings of the XI International Conference on Structural Dynamics (pp. 1545-1555). Athens: European Association for Structural Dynamics (EASD). doi:10.47964/1120.9125.19507
• Aksoy, T. (2015). TUNED VIBRATION ABSORBER DESIGN FOR A SUPPORTED HOLLOW CYLINDRICAL STRUCTURE. Ankara: MIDDLE EAST TECHNICAL UNIVERSITY.
• Bouna, H. S. and Nbendjo, B. R. (2012). Vibration Control of a Plate Subjected to Impulsive Force by Plate-Type Dynamic Vibration Absorbers. World Journal of Mechanics, 2, 143-151. doi:10.4236/wjm.2012.23017
• Wang, Q., Senatore, G., Jansen, K., Habraken, A. and Teuffel, P. (2020). Vibration Suppression Through Variable Stiffness and Damping Structural Joints. Frontiers in Built Environment, 6, 1-22. doi:10.3389/fbuil.2020.550864
• Chen, J., Chen, M. Z. and Hu, Y. (2021). Vortex-Induced Vibration Suppression of Bridges by Inerter-Based Dynamic Vibration Absorbers. Shock and Vibration, 2021, 1-18. doi:10.1155/2021/4431516
• Rubio, L., Loya, J. A., Miguélez, M. H. and Fernández-Sáez, J. (2013). Optimization of passive vibration absorbers to reduce chatter in boring. Mechanical Systems and Signal Processing, 41(1-2), 691-704. doi:10.1016/j.ymssp.2013.07.019
• Karam, M. A., Rezazadeh, G. and Ghaffari, S. (2015). An Investigation on Optimal Designing of Dynamic Vibration Absorbers Using Genetic Algorithm. Science Journal, 36, 765-779. Retrieved from https://www.researchgate.net/publication/286882651_An_Investigation_on_Optimal_Designing_of_Dynamic_Vibration_Absorbers_Using_Genetic_Algorithm
• Karimi, M., Shemshadi, M. and Firoozfam, N. (2020). A Simple method to design and analyze dynamic absorber using dimensional analysis. Journal of Vibration and Control,1(2), 73-81. doi:10.1177/1077546320923928
• Chesne´, S. (2021). Hybrid skyhook mass damper. Mechanics & Industry, 22(49), 1-10. doi:10.1051/meca/2021050
• EsmaiIzadeh, E. and Jalilj, N. (1998). Optimum Design of Vibration Absorbers for Structurally Damped Timoshenko Beams. Journal of Vibration and Acoustics,120, 833-841.
• Hu, Y. and Chen, M. Z. (2015). Performance evaluation for inerter-based dynamic vibration absorbers. International Journal of Mechanical Sciences,99, 297-307. doi:10.1016/j.ijmecsci.2015.06.003
• ASAMI, T., & YAMADA, K. (2021). Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞, H2, or stability criterion.Mechanical Engineering Journal,8(5), 21-00189. Retrieved on: 18/11/2022, Retrieved from: https://www.jstage.jst.go.jp/article/mej/8/5/8_21-00189/_pdf
• Feudo, S. L., Touzé, C., Boisson, J., & Cumunel, G. (2019). Nonlinear magnetic vibration absorber for passive control of a multi–storey structure.Journal of Sound and Vibration,438, 33-53. Retrieved on: 18/11/2022, Retrieved from: https://hal.archives-ouvertes.fr/hal-01891645/file/Lo_Feudo_et_al_2018V_revised_HAL.pdf
• Ha, S. I., & Yoon, G. H. (2021). Numerical and experimental studies of pendulum dynamic vibration absorber for structural vibration.Journal of Vibration and Acoustics,143(1). Retrieved on: 18/11/2022, Retrieved from: https://asmedc.silverchair.com/vibrationacoustics/article-pdf/143/1/011013/6559273/vib_143_1_011013.pdf
• Hua, Y., Wong, W., & Cheng, L. (2018). Optimal design of a beam-based dynamic vibration absorber using fixed-points theory.Journal of Sound and Vibration,421, 111-131. Retrieved on: 18/11/2022, Retrieved from: https://www.polyu.edu.hk/researchgrp/chengli/assets/pdf/197.pdf
• Infante, F., Kaal, W., Perfetto, S., & Herold, S. (2018, September). Design development of rotational energy harvesting vibration absorber (R-EHTVA). InSmart Materials, Adaptive Structures and Intelligent Systems(Vol. 51951, p. V002T07A001). American Society of Mechanical Engineers. Retrieved on: 18/11/2022, Retrieved from: https://www.researchgate.net/profile/Francesco-Infante/publication/327830955_Design_development_of_Rotational_Energy_Harvesting_Vibration_Absorber_R-EHTVA/links/5ba77597299bf13e60464f4a/Design-development-of-Rotational-Energy-Harvesting-Vibration-Absorber-R-EHTVA.pdf
• Ji, H., Zhao, X., Wang, N., Huang, W., Qiu, J., & Cheng, L. (2022). A Circular Eccentric Vibration Absorber With Circumferentially Graded Acoustic Black Hole Features.Journal of Vibration and Acoustics,144(2), 021014. Retrieved on: 18/11/2022, Retrieved from: https://www.researchgate.net/profile/Wei-Huang-199/publication/357715924_A_Circular_Eccentric_Vibration_Absorber_With_Circumferentially_Graded_Acoustic_Black_Hole_Features/links/61e12475c5e31033759184dd/A-Circular-Eccentric-Vibration-Absorber-With-Circumferentially-Graded-Acoustic-Black-Hole-Features.pdf
• Lang, Y., Tian, X., Kai, Y., & Hou, E. (2020, November). Stiffness and Mode Analysis of Framework for an Aerial Inertial Stabilized Platform. InJournal of Physics: Conference Series(Vol. 1635, No. 1, p. 012022). IOP Publishing. Retrieved on: 18/11/2022, Retrieved from: https://iopscience.iop.org/article/10.1088/1742-6596/1635/1/012022/pdf
• Luo, W., Lu, B., Zheng, H., Guo, Y., & Huang, T. (2019). A research of spinning machine: Effect of different structures of feed system on the static and dynamic characteristics.Advances in Mechanical Engineering,11(2), 1687814019828451. Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1687814019828451
• Noori, B., Arcos, R., Clot, A., & Romeu, J. (2019). Control of ground-borne underground railway-induced vibration from double-deck tunnel infrastructures by means of dynamic vibration absorbers.Journal of Sound and Vibration,461, 114914. Retrieved on: 18/11/2022, Retrieved from: https://upcommons.upc.edu/bitstream/handle/2117/174712/Noori,%20Behshad.%20Control%20of%20ground-borne%20underground%20railway-induced%20vibration%20from%20double-deck%20tunnel%20infrastructures%20by%20means%20of%20dynamic%20vibration%20absorbers.pdf?sequence=1
• Roozen, N. B., Urban, D., Piana, E. A., & Glorieux, C. (2021). On the use of dynamic vibration absorbers to counteract the loss of sound insulation due to mass-spring-mass resonance effects in external thermal insulation composite systems.Applied Acoustics,178, 107999. Retrieved on: 18/11/2022, Retrieved from: https://hal.archives-ouvertes.fr/hal-03202436/document
• Yang, F., Sedaghati, R., & Esmailzadeh, E. (2022). Vibration suppression of structures using tuned mass damper technology: A state-of-the-art review.Journal of Vibration and Control,28(7-8), 812-836. . Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1077546320984305
• Yoon, G.H., Choi, H. and So, H., 2021. Development and optimization of a resonance-based mechanical dynamic absorber structure for multiple frequencies.Journal of Low Frequency Noise, Vibration and Active Control,40(2), pp.880-897. Retrieved on: 18/11/2022, Retrieved from: https://journals.sagepub.com/doi/pdf/10.1177/1461348419855533
• Lang, Y., Tian, X., Kai, Y., & Hou, E. (2020, November). Stiffness and Mode Analysis of Framework for an Aerial Inertial Stabilized Platform. In Journal of Physics: Conference Series (Vol. 1635, No. 1, p. 012022). IOP Publishing.
• retrieve from: https://iopscience.iop.org/article/10.1088/1742-6596/1635/1/012022/pdf
• Luo, W., Lu, B., Zheng, H., Guo, Y., & Huang, T. (2019). A research of spinning machine: Effect of different structures of feed system on the static and dynamic characteristics. Advances in Mechanical Engineering, 11(2), 1687814019828451.
• retrieve from: https://journals.sagepub.com/doi/pdf/10.1177/1687814019828451
• Dai, L., Sun, H., Zhao, X., Wang, B., & Cao, J. (2021). Research on the Force Characteristics and Structural Optimization of Mine Antioutburst Door under the Influence of Coal and Gas Outburst Impact Airflow. Geofluids, 2021.
• retrieve from: https://www.hindawi.com/journals/geofluids/2021/5552949/
• ATLIHAN, G., OVALI, ?., & Abdullah, E. R. E. N. (2021). EKLEMEL? ?MALAT YÖNTEM?YLE ÜRET?LM?? BAL PETEKL? YAPILARIN T?TRE??M DAVRANI?LARININ NÜMER?K VE DENEYSEL OLARAK ?NCELENMES?. International Journal of 3D Printing Technologies and Digital Industry, 5(2), 98-108.
• retrieve from: https://dergipark.org.tr/en/download/article-file/1675731
• Bahrami, M. R., & Abed, S. A. (2019). Mechanics of robot inspector on electrical transmission lines conductors: performance analysis of dynamic vibration absorber. Vibroengineering Procedia, 25, 60-64. retrieve from: https://www.extrica.com/article/20807
• You, T., Zhou, J., Thompson, D. J., Gong, D., Chen, J., & Sun, Y. (2022). Vibration reduction of a high-speed train floor using multiple dynamic vibration absorbers. Vehicle System Dynamics, 60(9), 2919-2940.
• retrieve from:https://www.tandfonline.com/doi/full/10.1080/00423114.2021.1928248
• ASAMI, T., & YAMADA, K. (2021). Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞, H2, or stability criterion. Mechanical Engineering Journal, 8(5), 21-00189, retrieved from: https://www.jstage.jst.go.jp/article/mej/8/5/8_21-00189/_pdf
• Love, J. S., & Morava, B. (2021). Practical Experience with Full-scale Performance Verification of Dynamic Vibration Absorbers installed in Tall Buildings. International Journal of High-Rise Buildings, 10(2), 85-92, retrieved from: https://www.koreascience.or.kr/article/JAKO202117457616224.pdf
• Auleley, M., Thomas, O., Giraud-Audine, C., & Mahé, H. (2021). Enhancement of a dynamic vibration absorber by means of an electromagnetic shunt. Journal of Intelligent Material Systems and Structures, 32(3), 331-354, retrieved from: https://sam.ensam.eu/bitstream/handle/10985/22639/LISPEN_JIMSS_2020_THOMAS.pdf?sequence=2&isAllowed=y
• TOMIOKA, T., & HIGUCHI, K. (2021). Proposal and numerical feasibility study of a novel multi-modal and multi-axis dynamic vibration absorber consists of spherical viscoelastic material containing embedded ball-like mass. Mechanical Engineering Journal, 8(4), 21-00145, retrieved from: https://www.jstage.jst.go.jp/article/mej/8/4/8_21-00145/_pdf
• Qin, Y., Tan, J. J., & Hornikx, M. (2021, October). Reduction of low-frequency vibration of joist floor structures by multiple dynamic vibration absorbers: comparison of experimental and computational results. In Proceedings of Euronoise, retrieved from: http://ftp.sea-acustica.es/fileadmin/Madeira21/ID117.pdf
• Trujillo-Franco, L. G., Flores-Morita, N., Abundis-Fong, H. F., Beltran-Carbajal, F., Dzul-Lopez, A. E., & Rivera-Arreola, D. E. (2022). Oscillation Attenuation in a Building-like Structure by Using a Flexible Vibration Absorber. Mathematics, 10(3), 289, retrieved from: https://www.mdpi.com/2227-7390/10/3/289/pdf
• Cirelli, M., Gregori, J., Valentini, P. P., & Pennestrí, E. (2019). A design chart approach for the tuning of parallel and trapezoidal bifilar centrifugal pendulum. Mechanism and Machine Theory, 140, 711-729. Retrieved on: 19/11/2022, Retrieved from: https://www.researchgate.net/profile/Ettore-Pennestri/publication/334194064_A_Design_Chart_Approach_for_the_Tuning_of_Parallel_and_Trapezoidal_Bifilar_Centrifugal_Pendulum/links/5d1c6add458515c11c0ccb27/A-Design-Chart-Approach-for-the-Tuning-of-Parallel-and-Trapezoidal-Bifilar-Centrifugal-Pendulum.pdf
• Fernandez Escudero, C. (2021). Passive Aeroelastic control of aircraft wings via nonlinear oscillators (Doctoral dissertation, Polytechnique Montréal). Retrieved on: 19/11/2022, Retrieved from: https://publications.polymtl.ca/6578/1/2021_ClaudiaFernandezEscudero.pdf
• Fuqing, L., Chuanqiang, G., Zhen, L., Weiwei, Z., & Qiannan, X. (2022). Transonic flutter suppression with tuned mass damper by model-based stability analysis method. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 09544100221089704. Retrieved on: 19/11/2022, Retrieved from: https://www.researchgate.net/profile/Fuqing-Luo/publication/361984421_Transonic_flutter_suppression_with_tuned_mass_damper_by_model-based_stability_analysis_method/links/62cfe6147156f534a68299f7/Transonic-flutter-suppression-with-tuned-mass-damper-by-model-based-stability-analysis-method.pdf
• Javanshir, I., & Zarepour, G. (2021). Vibration analysis of fluid-structure interaction using tuned mass dampers. Journal of Applied Engineering Science, 19(2), 318-326. Retrieved on: 19/11/2022, Retrieved from: https://aseestant.ceon.rs/index.php/jaes/article/download/26043/16429
• Kolyshev, E. S., & Krapivko, A. V. (2019). Development of Computational and Experimental Methods for Determining Dynamic Characteristics of Aircraft Landing Gear. Retrieved on: 19/11/2022, Retrieved from: https://www.eucass.eu/doi/EUCASS2019-0502.pdf
• Li, L. (2021). Aircraft Noise Reduction Design Approaches (Doctoral dissertation, National Aviation University). Retrieved on: 19/11/2022, Retrieved from: https://dspace.nau.edu.ua/bitstream/NAU/55400/1/ASF_2021_134_LiLinfeng.pdf
• Lisitano, D., Bonisoli, E., Recchiuto, C. T., & Muscolo, G. G. (2021). Dynamic balance of the head in a flexible legged robot for efficient biped locomotion. Applied Sciences, 11(7), 2945. Retrieved on: 19/11/2022, Retrieved from: https://www.mdpi.com/2076-3417/11/7/2945/pdf
• Özyar, O., & Y?lmaz, Ç. (2021). A self-tuning adaptive-passive lever-type vibration isolation system. Journal of Sound and Vibration, 505, 116159. Retrieved on: 19/11/2022, Retrieved from: http://venus.santafe-conicet.gov.ar/ojs/index.php/mc/article/viewFile/6287/6353
• Pappalardo, C. M., & Guida, D. (2018). Development of a New Inertial-based Vibration Absorber for the Active Vibration Control of Flexible Structures. Engineering Letters, 26(3). Retrieved on: 19/11/2022, Retrieved from: http://www.engineeringletters.com/issues_v26/issue_3/EL_26_3_11.pdf
• Pokhrel, P. R., Lamsal, B., Kafle, J., & Kattel, P. (2020). Analysis of displacement of vibrating of mass spring due to opposition force. Tribhuvan University Journal, 35(1), 21-32. Retrieved on: 19/11/2022, Retrieved from: https://www.nepjol.info/index.php/TUJ/article/view/35830/28014
• Raze, G. (2021). Piezoelectric digital vibration absorbers for multimodal vibration mitigation of complex mechanical structures. Retrieved on: 19/11/2022, Retrieved from: https://orbi.uliege.be/bitstream/2268/256608/1/PhDThesis_GRaze.pdf
• Tian, W., Zhao, T., & Yang, Z. (2021). Metastructure plate with periodically embedded nonlinear vibration absorbers for nonlinear aeroelastic suppression. Retrieved on: 19/11/2022, Retrieved from: https://www.researchsquare.com/article/rs-364180/latest.pdf
• Tishhenko, I. V., Nikolaev, V. S., & Merkulov, V. I. (2020). Experimental study of the aircraft air cycle machine rotor dynamics on gas foil bearings. In MATEC Web of Conferences (Vol. 324, p. 03001). EDP Sciences. Retrieved on: 19/11/2022, Retrieved from: https://www.matec-conferences.org/articles/matecconf/pdf/2020/20/matecconf_cryogen2020_03001.pdf
• Xiao, X., He, Z. C., Li, E., & Cheng, A. G. (2019). Design multi-stopband laminate acoustic metamaterials for structural-acoustic coupled system. Mechanical Systems and Signal Processing, 115, 418-433. Retrieved on: 19/11/2022, Retrieved from: https://research.tees.ac.uk/ws/files/6455840/Design_multi_stopband_laminate_acoustic_metamaterials_for_structural_acoustic.pdf