Response analysis of nonlinear vibro-impact system coupled with viscoelastic force under colored noise excitations

2016 ◽  
Vol 86 ◽  
pp. 55-65 ◽  
Author(s):  
Deli Wang ◽  
Wei Xu ◽  
Xudong Gu ◽  
Haiqing Pei
Keyword(s):  
Colored Noise ◽  
Response Analysis ◽  
Impact System

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.

Stochastic Bifurcations of a Fractional-Order Vibro-Impact Oscillator Subjected to Colored Noise Excitation

2021 ◽  
Vol 31 (12) ◽  
pp. 2150177
Author(s):  
Ya-Hui Sun ◽  
Yong-Ge Yang ◽  
Ling Hong ◽  
Wei Xu
Keyword(s):  
Fractional Order ◽  
Colored Noise ◽  
Numerical Solutions ◽  
Gaussian White Noise ◽  
Research Work ◽  
Critical Conditions ◽  
Stochastic Bifurcation ◽  
Response Analysis ◽  
Impact Oscillator ◽  
Stochastic Bifurcations

A stochastic vibro-impact system has triggered a consistent body of research work aimed at understanding its complex dynamics involving noise and nonsmoothness. Among these works, most focus is on integer-order systems with Gaussian white noise. There is no report yet on response analysis for fractional-order vibro-impact systems subject to colored noise, which is presented in this paper. The biggest challenge for analyzing such systems is how to deal with the fractional derivative of absolute value functions after applying nonsmooth transformation. This problem is solved by introducing the Fourier transformation and deriving the approximate probabilistic solution of the fractional-order vibro-impact oscillator subject to colored noise. The reliability of the developed technique is assessed by numerical solutions. Based on the theoretical result, we also present the critical conditions of stochastic bifurcation induced by system parameters and show bifurcation diagrams in two-parameter planes. In addition, we provide a stochastic bifurcation with respect to joint probability density functions. We find that fractional order, coefficient of restitution factor and correlation time of colored noise excitation can induce stochastic bifurcations.

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