Moment Lyapunov exponent and stochastic stability of a vibro-impact system driven by Gaussian white noise

In this paper, the stochastic stability and pth moment Lyapunov exponent of a vibro-impact system driven by Gaussian white noise are studied. Firstly, the smooth stochastic dynamic system is given by introducing a non-smooth transformation. Thereafter, the first-order approximate solution of the pth moment Lyapunov exponent is obtained through applying the L.Arnold perturbation method, which are well consistent with those results calculated by the Monte Carlo simulation. Finally, the effects of the noise, the coefficient of restitution, the damping coefficient, and the natural frequency on the stochastic stability of the vibro-impact are discussed. Due to the existence of impact factor, the natural frequency has a significant effect on the stochastic stability of the system.