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.

Suppression of Limit Cycle Oscillations in a Van der Pol Oscillator by Means of a Passive Nonlinear Energy Sink

2005 ◽  
Author(s):  
Young S. Lee ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman ◽  
D. Michael McFarland
Keyword(s):  
Vibration Control ◽  
Limit Cycle ◽  
Nonlinear Energy Sink ◽  
Van Der Pol Oscillator ◽  
Numerical Continuation ◽  
Parameter Study ◽  
Limit Cycle Oscillations ◽  
Van Der Pol ◽  
Energy Sink ◽  
Nonlinear Energy

We present a study of passive but efficient vibration control, wherein a so-called nonlinear energy sink (NES) completely eliminates the limit cycle oscillations (LCOs) of a van der Pol oscillator. We first perform a parameter study in order to get overall understanding of responses with respect to parameters. Then, we establish a slow flow dynamics model to perform analytical study of the suppression mechanism which corresponds to classical nonlinear energy pumping, i.e., passive, broadband, and targeted energy transfer through 1:1 resonance capture. Utilizing the method of numerical continuation of equilibrium, we also study the bifurcation of the steady state solutions. It turns out that the system may have either subcritical or supercritical LCOs, and that for some parameter domain the LCOs are completely eliminated. This suggests applicability of the NES to vibration control in self-excited systems.

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.

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.

Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks

2006 ◽  
Vol 13 (1) ◽  
pp. 41-75 ◽  
Author(s):  
Young S. Lee ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman ◽  
D. Michael McFarland
Keyword(s):  
Limit Cycle ◽  
Van Der Pol Oscillator ◽  
Limit Cycle Oscillations ◽  
Van Der Pol ◽  
Non Linear

Probing the Force Field to Identify Potential Energy

2019 ◽  
Vol 86 (10) ◽  
Author(s):  
Yawen Xu ◽  
Lawrence N. Virgin
Keyword(s):  
Potential Energy ◽  
Ball Bearing ◽  
A Priori ◽  
Potential Energy Function ◽  
Mathematical Form ◽  
Restoring Force ◽  
Small Ball ◽  
Load Cells ◽  
The Hill ◽  
Small Steel

A small ball resting on a curve in a gravitational field offers a simple and compelling example of potential energy. The force required to move the ball, or to maintain it in a given position on a slope, is the negative of the vector gradient of the potential field: the steeper the curve, the greater the force required to push the ball up the hill (or keep it from rolling down). We thus observe the turning points (horizontal tangency) of the potential energy shape as positions of equilibrium (in which case the “restoring force” drops to zero). In this paper, we appeal directly to this type of system using both one- and two-dimensional shapes: curves and surfaces. The shapes are produced to a desired mathematical form generally using additive manufacturing, and we use a combination of load cells to measure the forces acting on a small steel ball-bearing subject to gravity. The measured forces, as a function of location, are then subject to integration to recover the potential energy function. The utility of this approach, in addition to pedagogical clarity, concerns extension and applications to more complex systems in which the potential energy would not be typically known a priori, for example, in nonlinear structural mechanics in which the potential energy changes under the influence of a control parameter, but there is the possibility of force probing the configuration space. A brief example of applying this approach to a simple elastic structure is presented.

Tunable Active Vibration Absorber: The Delayed Resonator

1995 ◽  
Vol 117 (4) ◽  
pp. 513-519 ◽  
Author(s):  
Nejat Olgac ◽  
Brian Holm-Hansen
Keyword(s):  
Transient Absorption ◽  
A Priori ◽  
Excitation Frequency ◽  
Vibration Absorber ◽  
Primary System ◽  
Active Vibration ◽  
Absorption Performance ◽  
Primary Focus ◽  
Novel Concept ◽  
Stability Issues

This paper elaborates upon a novel concept, the Delayed Resonator, a tunable active vibration absorber. This technique uses a control which has a time delayed feedback of the absorber mass displacement. The substance of this process is in that the absorber completely removes oscillations from the primary structure. Two very strong features that should be mentioned are: (a) the excitation frequency range can vary over a semi-infinite interval, and (b) the absorber can be tuned in real time. These are the unique characteristics of the technique distinguishing it from the others. Stability issues of the primary system combined with the Delayed Resonator are addressed following Nyquist and root locus methods. In particular, the absorption performance for cases with time varying excitation frequency is studied. The primary focus of this paper is on the analysis of transient absorption behavior of the Delayed Resonator during its tuning. An example case is provided which considers a step change in the excitation frequency. A well-pronounced manifestation of the tunability feature of the Delayed Resonator is observed. The superiority of the Delayed Resonator absorber over the conventional a priori tuned absorbers is also demonstrated.

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.

scholarly journals Flutter Control of a Two-Degrees-of-Freedom Airfoil Using a Nonlinear Tuned Vibration Absorber

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Arnaud Malher ◽  
Cyril Touzé ◽  
Olivier Doaré ◽  
Giuseppe Habib ◽  
Gaëtan Kerschen
Keyword(s):  
Limit Cycle ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Vibration Absorber ◽  
Aerodynamic Loads ◽  
Linear Approach ◽  
Aeroelastic Model ◽  
Large Amplitude Motions ◽  
Restoring Forces ◽  
Tuned Vibration Absorber

The influence of a nonlinear tuned vibration absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subcriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. Large amplitude motions of the airfoil are taken into account with nonlinear restoring forces for the pitch and plunge degrees-of-freedom. The two cases of a hardening and a softening spring behavior are investigated. The influence of each NLTVA parameter is studied, and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to shift the instability, avoid its possible subcriticality, and reduce the limit cycle oscillations (LCOs) amplitude.

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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