Abstract The stochastic response of frictionally damped strongly non-linear elastic impact oscillator subjected to white noise excitation and its stochastic bifurcation are considered. By the stochastic averaging method based on generalized harmonic function, one can obtain the stationary probability density function of this system. The effects of system parameters on the responses are investigated and the analytical results were verified by comparing with numerical results from Monte Carlo simulations. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that the coefficient of friction, damping constant of the elastic impact force respectively, can be treated as bifurcation parameters.

中文翻译：

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白噪声激发库仑摩擦强非线性弹性冲击系统随机分析

摘要 考虑了摩擦阻尼强非线性弹性冲击振荡器在白噪声激励下的随机响应及其随机分岔。通过基于广义调和函数的随机平均方法，可以得到该系统的平稳概率密度函数。研究了系统参数对响应的影响，并通过与蒙特卡罗模拟的数值结果进行比较来验证分析结果。随机分岔是通过平稳概率分布的质变来讨论的，这表明摩擦系数、弹性冲击力的阻尼常数分别可以作为分岔参数处理。