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

Stochastic Responses and Stability Analysis of Vibro-ImpactSystems With Friction Under Wideband Noise Excitation

研究了宽带噪声激励下碰撞摩擦系统的随机响应和概率为1渐近稳定性.基于非光滑变换和随机平均法得到了碰撞摩擦系统响应的稳态概率密度,并通过与Monte Carlo数值模拟结果对比,验证了上述解析方法的有效性.讨论了摩擦力和碰撞恢复系数对系统稳态概率密度的影响.基于平均Itô微分方程,得到其线性化方程的最大Lyapunov指数的表达式,通过Lyapunov指数确定系统平凡解的稳定性.结果表明,改变碰撞恢复系数和摩擦系数能调整系统的随机稳定性.

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 Itôequation 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.