scholarly journals A Principle of Similarity for Nonlinear Vibration Absorbers

2015 ◽  
Author(s):  
Giuseppe Habib ◽  
Gaetan Kerschen
Keyword(s):  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Engineering Systems ◽  
Restoring Force ◽  
Optimal Value ◽  
Real World Applications ◽  
Nonlinear Components ◽  
Principle Of Similarity ◽  
Tuned Vibration Absorber

With continual interest in expanding the performance envelope of engineering systems, nonlinear components are increasingly utilized in real-world applications. This causes the failure of well-established techniques to mitigate resonant vibrations. In particular, this holds for the linear tuned vibration absorber (LTVA), which requires an accurate tuning of its natural frequency to the resonant vibration frequency of interest. This is why the nonlinear tuned vibration absorber (NLTVA), the nonlinear counterpart of the LTVA, has been recently developed. An unconventional aspect of this absorber is that its restoring force is tailored according to the nonlinear restoring force of the primary system. This allows the NLTVA to extend the so-called Den Hartog’s equal-peak rule to the nonlinear range. In this work, a fully analytical procedure, exploiting harmonic balance and perturbation techniques, is developed to define the optimal value of the nonlinear terms of the NLTVA. The developments are such that they can deal with any polynomial nonlinearity in the host structure. Another interesting feature of the NLTVA, discussed in the paper, is that nonlinear terms of different orders do not interact with each other in first approximation, thus they can be treated separately. Numerical results obtained through the shooting method coupled with pseudo-arclength continuation validate the analytical developments.

scholarly journals Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber

2015 ◽  
Vol 471 (2176) ◽  
pp. 20140976 ◽  
Author(s):  
G. Habib ◽  
G. Kerschen
Keyword(s):  
Limit Cycle ◽  
A Priori ◽  
Numerical Continuation ◽  
Vibration Absorber ◽  
Primary System ◽  
Mathematical Form ◽  
Limit Cycle Oscillations ◽  
Van Der Pol ◽  
Restoring Force ◽  
Tuned Vibration Absorber

The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system.

The Influence Region Analysis for the Delayed Resonator Vibration Absorber

2001 ◽  
Author(s):  
Giulio Grillo ◽  
Nejat Olgac
Keyword(s):  
Vibration Suppression ◽  
Vibration Absorber ◽  
Primary System ◽  
Frequency Interval ◽  
Vibration Absorption ◽  
Region Analysis ◽  
The Common ◽  
Resonator Vibration ◽  
Three Degree Of Freedom ◽  
Tuned Vibration Absorber

Abstract This paper presents an influence region analysis for an actively tuned vibration absorber, the Delayed Resonator (DR). DR is shown to respond to tonal excitations with time varying frequencies [1–3]. The vibration suppression is most effective at the point of attachment of the absorber to the primary structure. In this study we show that proper feedback control on the absorber can yield successful vibration suppression at points away from this point of attachment. The form and the size of such “influence region” strongly depend on the structural properties of the absorber and the primary system. There are a number of questions addressed in this paper: a) Stability of vibration absorption, considering that a single absorber is used to suppress oscillations at different locations. b) Possible common operating frequency intervals in which the suppression can be switched from one point on the structure to the others. A three-degree-of-freedom system is taken for as example case. One single DR absorber is demonstrated to suppress the oscillations at one of the three masses at a given time. Instead of an “influence region” a set of “influence points” is introduced. An analysis method is presented to find the common frequency interval in which the DR absorber operates at all three influence points.

Recent Studies of Adaptive Tuned Vibration Absorbers/Neutralizers

2009 ◽  
Vol 62 (6) ◽  
Author(s):  
Lari Kela ◽  
Pekka Vähäoja
Keyword(s):  
Piezoelectric Materials ◽  
Helmholtz Resonator ◽  
Primary System ◽  
Vibration Absorbers ◽  
Review Section ◽  
Helmholtz Resonators ◽  
Tuned Vibration Absorbers ◽  
Current Events ◽  
Year 2000 ◽  
Tuned Vibration Absorber

This article gathers together the most recent articles of adjustable tuned vibration absorbers. The tuned vibration absorber was invented over 100 years ago, and its adjustability is also already well-known. However, concentration of this review was only on articles published since the year 2000 in peer reviewed journals, except from certain elementary books and some previous review articles in order to keep up with the current events in this broad field. First a brief inspection of the theory of tuned vibration absorbers (TVAs) is presented. After that mechanical TVAs are presented more carefully. In the same chapter the following are also handled: virtual absorbers, absorbers with adjustable damping, and Helmholtz resonators. Own chapter is allocated for multiple TVAs whose idea is to replace adjustability by adding several TVAs to primary system to damp out vibrations in the wide frequency band. The review section is completed by presenting smart material TVAs, which include, e.g., piezoelectric materials, shape-memory alloys, electrorheological and magnetorheological materials of fluids. An adjustable Helmholtz resonator in a low pressure hydraulic system is presented in Sec. 5. Experiments verify the efficiency of the damping character of the adjustable Helmholtz resonator whose resonant frequency can be varied.

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

2021 ◽  
pp. 107754632110382
Author(s):  
Peng Sui ◽  
Yongjun Shen ◽  
Shaopu Yang ◽  
Junfeng Wang
Keyword(s):  
Analytical Solution ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

scholarly journals Friction-Induced Vibration Suppression via the Tuned Mass Damper: Optimal Tuning Strategy

Lubricants ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 100
Author(s):  
Jia Lin Hu ◽  
Giuseppe Habib
Keyword(s):  
Vibration Suppression ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Restoring Force ◽  
Stick Slip ◽  
Optimal Tuning ◽  
Dynamic Vibration ◽  
Tuning Strategy ◽  
Friction Induced Vibration

Friction-induced vibrations are a significant problem in various engineering applications, while dynamic vibration absorbers are an economical and effective tool for suppressing various kinds of vibrations. In this study, the archetypal mass-on-moving-belt model with an attached dynamic vibration absorber was considered. By adopting an analytical procedure, the optimal tuning of the absorber’s parameters was defined. Furthermore, the bifurcations occurring at the loss of stability were analytically investigated; this analysis illustrated that a properly chosen nonlinearity in the absorber’s stiffness permits controlling the supercritical or subcritical character of the bifurcation. However, a numerical analysis of the system’s dynamics, despite confirming the analytical results, also illustrated that the system’s global behavior is only slightly affected by the bifurcation character. Indeed, a dynamic vibration absorber possessing a perfectly linear restoring force function seems to provide the optimal performance; namely, it minimizes the velocity range for which stick–slip oscillations exists.

scholarly journals Study of Magnetic Vibration Absorber with Permanent Magnets along Vibrating Beam Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
F. B. Sayyad ◽  
N. D. Gadhave
Keyword(s):  
Cantilever Beam ◽  
Gas Turbines ◽  
Permanent Magnets ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Vibratory System ◽  
Electrical Generator

The vibration absorbers are frequently used to control and minimize excess vibration in structural system. Dynamic vibration absorbers are used to reduce the undesirable vibration in many applications such as pumps, gas turbines, engine, bridge, and electrical generator. To reduce the vibration of the system, the frequency of absorber should be equal to the excitation frequency. The aim of this study is to investigate the effect of magnetic vibration absorber along vibrating cantilever beam. This study will aim to develop a position of magnetic vibration absorber along the cantilever beam to adopt the change in vibratory system. The absorber system is mounted on a cantilever beam acting as the primary system. The objective is to suppress the vibration of the primary system subjected to a harmonic excitation whose frequencies are varying. It can be achieved by varying the position of magnetic vibration absorber along the length of beam. The advantage of magnetic vibration absorber is that it can be easily tuned to the excitation frequency, so it can be used to reduce the vibration of system subjected to variable excitation frequency.

Implementation of a Nonlinear Torsional Vibration Absorber for Suppression of Vibrations in Rotating Machinery

2013 ◽  
Author(s):  
Ammaar Bin Tahir ◽  
Oleg Shiryayev ◽  
Nader Vahdati ◽  
Hamad Karki
Keyword(s):  
Nonlinear Vibration ◽  
Torsional Vibration ◽  
Vibration Suppression ◽  
Nonlinear Energy Sink ◽  
Modal Parameters ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Modal Model ◽  
Linear Spring

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is tuned for a specific resonant frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies. Vibrations dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. Experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, we carry out the design optimization of the nonlinear torsional vibration absorber using an equivalent 2-DOF modal model. A linear vibration absorber is developed in parallel. Subsequently, both absorbers will be manufactured, assembled and mounted on the system to evaluate their vibration suppression capabilities.

Control of a Tuned Vibration Absorber Based on SMA Wires

2005 ◽  
Author(s):  
Eric Williams ◽  
Mohammad H. Elahinia ◽  
Jeong-Hoi Koo
Keyword(s):  
Shape Memory ◽  
Natural Frequency ◽  
Constitutive Relations ◽  
Robustness Analysis ◽  
Vibration Absorber ◽  
Primary System ◽  
Frequency Change ◽  
Simulation Results ◽  
Close Loop Control ◽  
Tuned Vibration Absorber

This paper presents the control simulation results of a tuned vibration absorber (TVA) that utilizes the properties of shape memory alloy (SMA) wires. A conventional passive TVA is effective when it is precisely tuned to the frequency of a vibration mode; otherwise, resonance may occur that could damage the system. Additionally, in many applications the frequency of the primary system often changes over time. For example, the mass of the primary system can change causing a change in its natural frequency. This frequency change of the primary system can significantly degrade the performance of the TVA. To cope with this problem, many alternative TVA’s (such as semiactive, adaptive, and active TVA’s) have been studied. As another alternative, this paper investigates the use of Shape Memory Alloys (SMA’s) in passive TVA’s in order to improve the robustness of the TVA’s subject to mass change in the primary system. This allows for effective tuning of the stiffness of the TVA to adapt to the changes in the primary system’s natural frequency. To this end, a close-loop control system adjusts the applied current to the SMA wires in order to maintain the desired stiffness. The model, presented in this paper, contains the dynamics of the TVA along with the SMA wire model that includes phase transformation, heat transfer, and the constitutive relations. The closed-loop robustness analysis is performed for the SMA-TVA and is compared with the equivalent passive TVA. For the robustness analysis, the mass of the primary system is varied by ± 30% of its nominal mass. The simulation results show that the SMA-TVA is more robust than the equivalent passive TVA in reducing peak vibrations in the primary system subject to change of its mass.

Design of a non-linear vibration absorber

2012 ◽  
Vol 3 (2) ◽  
pp. 111-115
Author(s):  
M. Geeroms ◽  
M. Marijns ◽  
M. Loccufier ◽  
D. Aeyels
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Fourier Series Expansion ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Linear Vibration ◽  
Restoring Force ◽  
Nonlinear Dynamical

Linear vibration absorbers can only capture certain discrete frequencies. Therefore the useof nonlinear vibration absorbers which can capture a whole range of frequencies is investigated asan alternative. Such a nonlinear vibration absorber has some special characteristics. For examplethere is a certain frequency-energy dependence. To investigate nonlinear dynamical systems thereis a need for new methods. The harmonic balance method is such a method and is discussed. Theidea is to substitute a Fourier series expansion of the solution variables into the system equations and’balance’ them. Furthermore two realisations of a nonlinear energy sink as an example of a nonlinearvibration absorber are discussed. One based on the restoring force in a wire, the other one by forcinga linear spring to follow a certain path. As will be discussed, an analog principle can be used for therealisation of a Duffing type of nonlinear absorber.

Tonal Tuning of a Variable Inertia Vibration Absorber: A Feasibility Study

2003 ◽  
Author(s):  
Behrooz Fallahi ◽  
Said Megahed ◽  
Mohammed Seif
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Nonlinear Model ◽  
Dynamic Equations ◽  
Vibration Absorber ◽  
Primary System ◽  
Moving Mass ◽  
New Class ◽  
Linearized Model ◽  
Tuned Vibration Absorber

The primary goal of this study is to investigate the dynamics of a new class of adaptive Tuned Vibration Absorber (TVA): A variable effective inertia absorber. In particular, the accuracy of linearization of the dynamic equations, the effect of the moving mass on the dynamics of the absorber, and steady state vibration of the primary system are investigated. It is shown that the linearized model is accurate. Two simulations using the nonlinear model are reported. These simulations show effectiveness of the absorber on reducing the displacement and acceleration of the primary system. In a third simulation, the block is moved from a detuned position to a tuned position and nonlinear differential equation of the motion is solved. The results show a significant decrease of the vibration of the primary system.

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