Modeling of the mean Poincaré map on a class of random impact oscillators

In this paper, a class of random vibro-impact systems is studied. For this class of random systems, the general discrete-time model of systems described by mean of impact Poincarè map have been derived. Two engineering examples: a marine engine resiliently mounted under shock excitation and a stochastic rattling system have been investigated. The calculated results show that those models can reveal complex nonlinear behaviors. The bifurcation diagrams exhibit the routes to random chaos.