Response spectral densities of strongly nonlinear systems under random excitation

A new analytical procedure is developed to evaluate the response spectral densities for nonlinear systems excited by Gaussian white noises or filtered Gaussian white noises. The cumulant-neglect closure scheme is applied to truncate the governing differential equations for statistical moments of the response variables at two different times. The truncated equations in the time domain are transformed to a set of linear algebraic equations in the frequency domain, which include the response spectral densities as unknowns. This new procedure is illustrated in the example of a Duffing oscillator, and analytical results are compared with those obtained from Volterra series method and Monte Carlo simulations.