Stochastic Stability of a One-Sided Vibro-Impact System Excited by Real Noise

Vibro-impact is widespread in practical engineering, so it is of great practical significance to study it. However, research on the stochastic stability and bifurcation of vibro-impact systems is still limited, especially regarding moment stability. Based on the pth moment Lyapunov exponent, this paper investigates the stochastic stability of a vibro-impact system driven by real noise. First, a smooth stochastic dynamical system is obtained through a non-smooth transformation, and the Ornstein-Uhlenbeck process is employed to characterize the real-noise model. On this basis, a second-order approximate solution of the pth moment Lyapunov exponent is derived using the L. Arnold perturbation method, showing good agreement with Monte Carlo simulation results. Finally, the effects of noise parameters, natural frequency, restitution coefficient, and damping coefficient on the stochastic stability of vibro-impact vibrations are analyzed. Owing to the presence of impact factors, the natural frequency has a direct and significant influence on the stochastic stability of the system.