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.

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

Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink

2018 ◽  
Vol 95 (2) ◽  
pp. 1435-1456 ◽  
Author(s):  
K. Zhou ◽  
F. R. Xiong ◽  
N. B. Jiang ◽  
H. L. Dai ◽  
H. Yan ◽  
...  
Keyword(s):  
Vibration Control ◽  
Nonlinear Vibration ◽  
Nonlinear Energy Sink ◽  
Nonlinear Vibration Control ◽  
Energy Sink ◽  
Nonlinear Energy

Vibration control of a nonlinear beam with a nonlinear energy sink

2015 ◽  
Vol 83 (1-2) ◽  
pp. 1-22 ◽  
Author(s):  
M. Kani ◽  
S. E. Khadem ◽  
M. H. Pashaei ◽  
M. Dardel
Keyword(s):  
Vibration Control ◽  
Nonlinear Energy Sink ◽  
Nonlinear Beam ◽  
Energy Sink ◽  
Nonlinear Energy

scholarly journals Frequency-Energy Plots of Bistable Nonlinear Energy Sink

2021 ◽  
Author(s):  
Mohammed Ameen Al Shudeifat ◽  
Adnan Salem Saeed
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Energy Levels ◽  
Dynamical Behavior ◽  
Nonlinear Energy Sink ◽  
Low Energy ◽  
Unstable Equilibrium ◽  
Numerical Continuation ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as Bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency-energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out of- phase backbone branches, especially at low energy levels. The wavelet transform is imposed into the FEP for variety of initial conditions and damping content and it is found that the FEP has backbone branches at low energy levels associated with the oscillation of the bistable attachments about one of its stable equilibrium positions where passage through the unstable equilibrium position does not occur.

Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

2022 ◽  
Author(s):  
Mohammad Al-Shudeifat ◽  
Adnan Saeed
Keyword(s):  
Dynamical Systems ◽  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Dynamical Behaviour ◽  
Subharmonic Resonance ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Linear Dynamical Systems ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

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