Nonstationary Response Analysis of a Duffing Oscillator by the Wiener-Hermite Expansion Method

The Wiener-Hermite functional series expansion method is used to analyze the nonstationary response of a Duffing oscillator under random excitations. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite kernel functions is described. The first three terms in the series are retained. The nonstationary response of a damped Duffing oscillator subjected to a modulated white noise is studied. For several values of nonlinearity strength and different damping coefficients the nonstationary mean-square responses are obtained. The results are compared with those found by a single-term expansion and other methods. It is shown that mean-square responses obtained by the three-term expansion agree with the exact stationary variances and the simulation results.