Abstract
Vibro-impact phenomena are prevalent in practical engineering, making research on their stochastic dynamic characteristic of great practical significance. However, the research on stochastic stability and bifurcation of vibro-impact systems is still limited, especially the moment stability. In this paper, based on the pth moment Lyapunov exponent, the stochastic stability of a vibro-impact system driven by non-Gaussian colored noise is investigated. Firstly, the smooth stochastic dynamic system is obtained making use of a non-smooth transformation and the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process by utilizing the path-integral method. Thereafter, through applying the L.Arnold perturbation method, the second-order approximate solution of the pth moment Lyapunov exponent is calculated, which agree well with the simulation results given by the Monte Carlo method. Finally, the effects of the noise parameters, natural frequency, coefficient of restitution, and damping coefficient on the stochastic stability of the vibro-impact are studied. Due to the existence of impact factor, the natural frequency has a direct and significant effect on the stochastic stability of the system.
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