Stochastic Responses of Duffing-Van Der Pol Vibro-Impact Oscillator with Colored Noise

摘要

The purpose of this work is to use the stochastic averaging method to study the response of a vibro-impact system excited by additive and multiplicative colored noises. The non-smooth transformation of state variables is used to transform the vibro-impact system to a new system without impact term. And Fourier series is applied to obtain the stationary probability density function. The validity of the analytical results is verified by the numerical simulations. Moreover, stochastic P-bifurcations are also explored.