Response of a Duffing - Rayleigh system with a fractional derivative under Gaussian white noise excitation

In this paper, we consider the response analysis of a Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed.