A practical technique for spectral analysis of nonlinear systems under stochastic parametric and external excitations

A practical approach is developed for analyzing the spectral response of a nonlinear system subjected to both parametric and external Gaussian white noise excitations. The technique is implemented through the combined methods of equivalent external excitation and equivalent linearization to derive an equivalent linear system under equivalent external noise excitation. The spectral response is obtained through utilizing the input-output spectral relation and covariance matching condition. A parametric noise excited linear system, Duffing oscillator, and nonlinear system with hysteretic nonlinearity are selected for investigation. The validity of the method for analyzing spectral response is further supported by some analytical solutions and by the fast Fourier transform (FFT) technique through Monte Carlo simulations.