Random vibrations of Rayleigh vibroimpact oscillator under Parametric Poisson white noise

• Random vibration problems for Rayleigh vibroimpact system with a rigid barrier are considered.
• The random excitation is Parametric Poisson white noise.
• The averaged generalized Fokker-Planck-Kolmogorov equations for vibroimpact system with parametric Poisson white noise are derived.
• The approximate stationary responses are solved by perturbation method.
• Effects on the response for different damping coefficients, restitution coefficients and noise intensities are discussed.

Random vibration problems for a single-degree-of-freedom (SDOF) Rayleigh vibroimpact system with a rigid barrier under parametric Poisson white noise are considered. The averaged generalized Fokker-Planck-Kolmogorov (FPK) equations with parametric Poisson white noise are derived after using the nonsmooth variable transformation and the approximate stationary solutions for the system's response are obtained by perturbation method. The results are validated numerically by using Monte Carlo simulations from original vibroimpact system. Effects on the response for different damping coefficients, restitution coefficients and noise intensities are discussed. Furthermore, stochastic bifurcations are also explored.