Stochastic Dynamics of a Unilateral Vibro-impact System Driven by Gaussian White Noise

Vibro-impact has the vital influence on the dynamic properties, reliability and service life of the system, which exists widely in mechanical systems. The purpose of this paper is to investigate the stochastic stability of a unilateral vibro-impact system by solving the pth moment Lyapunov exponent and the largest Lyapunov exponent. Firstly, a stochastic dynamic model of the unilateral vibro-impact system under Gaussian white noise excitation is constructed. Then, the vibro-impact system is transformed into a smooth dynamic system by utilizing the Zhuravlev transformation. Thereafter, the perturbation method is utilized to derive the approximate analytical solution of the pth moment Lyapunov exponent, which is in excellent agreement with the numerical simulation result. The largest Lyapunov exponent and moment stability index are determined by further extension. Finally, this paper analyzes the impact of system parameters and noise on the stability of the system. Based on the obtained Lyapunov exponents, strategies to enhance system stability are proposed.