On a response of the stochastic rayleigh system

The paper shows that the response of the random Rayleigh system, which is under harmonic and random excitations, can be found by a system of algebraic equations. The analytical approach is based on the stochastic averaging method and equivalent linearization method in Cartesian coordinates so that the Fokker-Planck equation associated with the linear equations obtained can be solved exactly by the technique of auxiliary function. The harmonic excitation frequency is taken to be in the neighborhood of the system natural frequency. The mean-square responses obtained by the proposed approach are compared with those obtained by Monte Carlo simulation method.