Random responses analysis of friction systems with viscoelastic forces under Gaussian colored noise excitation

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 functions 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-bifurcations, 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.