Abstract:A one-degree-of-freedom vibro-impact system with clearance is established. The analytic expression of Poincaré map of the system is derived, and the spectrum of Lyapunov exponents of the system is calculated numerically, the effects of the dynamical behavior of vibro-impact system with random disturbance is analyzed. At last, with the largest Lyapunov exponent, the stochastic bifurcation of random non-smooth system is studied. Numerical simulations show that period-doubling bifurcation also exists in the random non-smooth system, but is different from that in the deterministic system.