中文摘要：

研究了Gauss色噪声激励下含黏弹力、弱非线性阻尼的摩擦振子的随机响应.将适用于光滑系统的随机平均法推广到了非光滑摩擦系统,进而得到系统振幅、位移及速度的稳态概率密度函数.同时结合材料的黏弹性,研究了摩擦力和Gauss色噪声对系统响应的影响.研究表明,摩擦力、黏弹力及噪声项的相关参数均可引起随机P-分岔,并且在一定范围内系统响应对摩擦力极为敏感.此外,理论结果与Monte Carlo模拟结果吻合较好,验证了方法的有效性.

英文摘要：

The stochastic responses of non-linearly damped friction oscillators with viscoelastic forces under Gaussian colored noise excitation were investigated. The stochastic averaging method, which is applicable to smooth systems, was extended to non-smooth friction systems, and the stationary probability density tractions of the amplitude, displacement and velocity of the system were obtained. In view of the material viscoelastic properties, the effects of friction and Gaussian colored noise on the responses of the system were studied. The study shows that the parameters of friction force, viscoelastic force and noise may induce stochastic P-bifurca- tions, and the system responses are very sensitive to the friction force in a certain range. In addition, the theoretical results are in good agreement with the Monte Carlo simulation results, which verifies the rationality of the proposed method.