Response analysis of Rayleigh–Van der Pol vibroimpact system with inelastic impact under two parametric white-noise excitations

2015 ◽  
Vol 82 (4) ◽  
pp. 1797-1810 ◽  
Author(s):  
Guidong Yang ◽  
Wei Xu ◽  
Jinqian Feng ◽  
Xudong Gu
Keyword(s):  
White Noise ◽  
Response Analysis ◽  
Van Der Pol ◽  
Inelastic Impact ◽  
Vibroimpact 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.

scholarly journals Stochastic Responses of Lightly Nonlinear Vibroimpact System with Inelastic Impact Subjected to External Poisson White Noise Excitation

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Guidong Yang ◽  
Wei Xu ◽  
Dongmei Huang ◽  
Mengli Hao
Keyword(s):  
White Noise ◽  
Coordinate Transformation ◽  
Perturbation Technique ◽  
Inverse Transformation ◽  
Poisson White Noise ◽  
Dirac Delta ◽  
White Noise Excitation ◽  
Inelastic Impact ◽  
Fpk Equation ◽  
Vibroimpact System

A procedure for analyzing stationary responses of lightly nonlinear vibroimpact system with inelastic impact subjected to external Poisson white noise excitation is proposed. First, the original vibroimpact system is transformed to a new system without velocity jump in terms of the Zhuravlev nonsmooth coordinate transformation and the Dirac delta function. Second, the averaged generalized Fokker-Planck-Kolmogorov (FPK) equation for transformed system under parametric excitation of Poisson white noise is derived by stochastic averaging method. Third, the averaged generalized FPK equation is solved by using the perturbation technique and inverse transformation of the Zhuravlev nonsmooth coordinate transformation to obtain the approximately stationary solutions for response probability density functions of original vibroimpact system. Last, analytical and numerical results for two typical lightly nonlinear vibroimpact systems are presented to assess the effectiveness of the proposed method. It is found that they are in good agreement and the proposed method is quite effective.

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.

Discrete Evolutionary Spectra of Discretized Beams and Plates Under Time-Frequency Modulated Random Excitations

1995 ◽  
Author(s):  
C. W. S. To ◽  
H. W. Hung
Keyword(s):  
White Noise ◽  
Linear Time ◽  
Response Analysis ◽  
Plate Structures ◽  
Time Frequency ◽  
Linear Time Invariant ◽  
Practical Engineering ◽  
Band Limited ◽  
Evolutionary Spectra ◽  
Time Invariant

Abstract Various methods that employed the theory of evolutionary spectral density of Priestley (1965) have been proposed for the non-stationary random response analysis of linear time-invariant multi-degree-of-freedom systems (Hammond, 1968, Fugimori and Lin, 1973, To, 1982, Shihab and Preumont, 1987, To and Hung, 1989). In this paper the method presented earlier by the authors (1989) is further applied to discrete or discretized systems under time-frequency moduated random excitations in which the white noise processes are replaced by band-limited white noise processes and Kanai-Tajimi models. Applications of the method to beam and plate structures discretized by the finite element method are made so as to illustrate its capability in dealing with practical engineering systems under intensive transient disturbances that may be modelled as such time-frequency modulated random excitations.

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