宽带噪声激励下碰撞摩擦系统的 随机响应和稳定性的研究.

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 system. 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 system responses were studied. Furthermore, The Lyapunov exponent of the linearized averaged It8 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 stochastic stability [ABSTRACT FROM AUTHOR]