Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback

2003 ◽  
Vol 38 (1) ◽  
pp. 123-131 ◽  
Author(s):  
Attilio Maccari
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
State Feedback ◽  
Primary Resonance ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

Quenching of Self-Excited Vibrations

1989 ◽  
Vol 111 (2) ◽  
pp. 130-133 ◽  
Author(s):  
K. R. Asfar
Keyword(s):  
Control System ◽  
Vibration Control ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Passive Vibration Control ◽  
First Order ◽  
System A ◽  
Excited System ◽  
Excited Vibration ◽  
First Order Perturbation

A passive vibration control system for the quenching of undesirable self-excited vibrations in mechanical systems is presented. The system is a Lanchester damper, attached to the main self-excited system; a van der Pol oscillator. A first-order perturbation solution shows that complete quenching of self-excited vibration is possible. The result is verified by numerical integration of the governing differential equations. Furthermore, the damper is shown to be effective in suppressing forced self-excited vibrations.

Nonlinear primary resonance in vibration control of cable-stayed beam with time delay feedback

2020 ◽  
Vol 137 ◽  
pp. 106488 ◽  
Author(s):  
Jian Peng ◽  
Mingjiao Xiang ◽  
Lianhua Wang ◽  
Xianzhong Xie ◽  
Hongxin Sun ◽  
...  
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Primary Resonance

Bifurcation Control Of A Fractional-Order Van Der Pol Oscillator Based On The State Feedback

2014 ◽  
Vol 17 (5) ◽  
pp. 1756-1766 ◽  
Author(s):  
Min Xiao ◽  
Guoping Jiang ◽  
Wei Xing Zheng ◽  
Senlin Yan ◽  
Youhong Wan ◽  
...  
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
The State ◽  
Bifurcation Control ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

Bifurcation Control for a Kind of Non-Autonomous System with Time Delay

2010 ◽  
Vol 34-35 ◽  
pp. 1752-1756
Author(s):  
Chang Zhao Qian ◽  
Zhi Wen Wang ◽  
Chuang Wen Dong ◽  
Yang Liu
Keyword(s):  
Time Delay ◽  
Perturbation Method ◽  
Time Delays ◽  
Autonomous System ◽  
Primary Resonance ◽  
Stable Region ◽  
Bifurcation Equation ◽  
Van Der Pol ◽  
Average Equation ◽  
System With Time Delay

A forced van der Pol system with two time-delays is studied. The central aim is analyzing primary resonance of this system. Perturbation method is used to obtain the average equation and bifurcation equation with time-delays. Based on the average equation, the stable region of this system is discussed. Based on the bifurcation equation, the multivalued property of response amplitude is studied. The result indicates that this system can be well controlled with time delays.

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