Nonstationary random vibration of a Duffing oscillator is considered. The method of Wiener-Hermite series expansion of an arbitrary random function is reviewed and applied to the analysis of the response of a Duffing oscillator. Deterministic integral equations for the Wiener-Hermite kernel functions are derived and discussed. For the special case of a shaped white-noise excitation, the system of integral equations are solved by an iterative scheme and the mean square responses of a Duffing oscillator for various values of nonlinearity strength and damping coefficient are calculated and the results are elaborated in several graphs.

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