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

This paper aims to investigate stochastic dynamics of nonlinear vibro-impact system with viscoelastic term subjected to wide-band noise. Firstly, the viscoelastic term is approximated as equivalent damping and stiffness forces. Then, the non-smooth transformation is adopted to convert the vibro-impact system into a system without barriers. By using of the stochastic averaging method based on generalized harmonic function, the probability densities of the stationary response are obtained and dynamical influence of viscoelastic parameters and restitution coefficient of the system are discussed as well. Comparison between the analytical simulation and numerical simulation results shows an excellent agreement.