Probabilistic responses of three-dimensional stochastic vibro-impact systems

Chatter between devices becomes a primary concern in actual engineering problems since it may cause the reduction of efficiency. Due to random factors and non-smooth properties, difficulties rest in deriving the analytical results and such systems are generally investigated with simplified approximate methods. In this context, the present paper pioneers the response analysis of three-dimensional hydraulic relief valve impact systems under stochastic excitations. In order to retain the non-smooth characteristics of the systems under consideration, no non-smooth transformation is imposed on the original system. A procedure in which the stochastic trajectories start from the contact surface and return to the contact surface for the next time is constructed. Probability density functions (PDFs) of the random trajectories returning to the contact surface at any time can be obtained, and the proposed procedure is proved accurate and efficient using Monte Carlo (MC) simulations in this paper. Moreover, we find that the flow rate of the systems can lead to the stochastic P-bifurcation on the contact surface. Further discussion indicates that the proposed procedure can substantially reflect the complicated dynamic behaviors of the high-dimensional vibro-impact systems.