The stochastic responses and the asymptotic stability with probability 1 of vibro-impact systems with friction under wideband noise excitation were investigated.The Zhuravlev non-smooth transformation and the stochastic averaging method were extended to obtain the steady-state probability density functions of the sys-tem.The accuracy of the method was verified through comparison of the theoretical results with those from the Monte Carlo simulations.The effects of the friction force and the vibro-impact restitution coefficient on the sys-tem responses were studied.Furthermore,The Lyapunov exponent of the linearized averaged Itô equation was derived and the stability of the trivial solution was determined with the Lyapunov exponent.The results show that,changing the frictional coefficient and the vibro-impact restitution coefficient could adjust the system sto-chastic stability.
关键词
碰撞摩擦系统/随机平均法/稳态响应/随机稳定性
Key words
vibro-impact system with friction/stochastic averaging method/steady state response/stochastic stability
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