Stochastic response of Duffing-Van der Pol vibro-impact system with viscoelastic term under wide-band excitation

2017 ◽  
Vol 104 ◽  
pp. 748-757 ◽  
Author(s):  
Li Liu ◽  
Wei Xu ◽  
Xiaole Yue ◽  
Qun Han
Keyword(s):  
Wide Band ◽  
Stochastic Response ◽  
Van Der Pol ◽  
Impact System ◽  
Viscoelastic Term

Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise

2018 ◽  
Vol 28 (13) ◽  
pp. 1830043 ◽  
Author(s):  
Meng Su ◽  
Wei Xu ◽  
Guidong Yang
Keyword(s):  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Response Analysis ◽  
State Variables ◽  
Van Der Pol ◽  
Impact System ◽  
The Impact

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

Stationary Response of Duffing-van der Pol Oscillator with Delayed Feedback Control under Wide-Band Noise Excitation

2013 ◽  
Vol 300-301 ◽  
pp. 1518-1524
Author(s):  
Peng Lin ◽  
Chang Shui Feng ◽  
Qiao Yi Wang
Keyword(s):  
Feedback Control ◽  
Wide Band ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Stationary Response ◽  
Wide Band Noise ◽  
Time Delayed Feedback

The stationary response of Duffing-van der Pol oscillator with time-delayed feedback control under wide-band noise excitations is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method. Finally, the stationary response of the system is obtained by solving the Fokker-Plank-Kolmogorov equation associated with the averaged Itô equation. The effect of time delay in feedback control force on the response is analyzed. The theoretical results are well verified through digital simulation.

Stochastic Response of a Vibro-Impact System by Path Integration Based on Generalized Cell Mapping Method

2014 ◽  
Vol 24 (10) ◽  
pp. 1450129 ◽  
Author(s):  
Chao Li ◽  
Wei Xu ◽  
Xiaole Yue
Keyword(s):  
White Noise ◽  
Mapping Method ◽  
Cell Mapping ◽  
Van Der Pol ◽  
Generalized Cell Mapping ◽  
White Noise Excitation ◽  
Impact System ◽  
Steady State Responses ◽  
State Responses ◽  
Transient And Steady State

The generalized cell mapping method is extended to study the response of a vibro-impact system with white noise excitation. The transient and steady-state responses of a Duffing–van der Pol vibro-impact system under white noise excitation are obtained by using this method. The accuracy of the method is verified by comparison with Monte Carlo simulation results. In addition, stochastic P-bifurcation for different parameters is considered, and several special forms are observed in this paper.

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