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

[+] Author and Article Information
I. I. Orabi, G. Ahmadi

Department of Mechanical and Industrial Engineering, Clarkson University, Potsdam, NY 13676

J. Appl. Mech 54(2), 434-440 (Jun 01, 1987) (7 pages) doi:10.1115/1.3173033 History: Received February 24, 1986; Revised July 31, 1986; Online July 21, 2009


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.

Copyright © 1987 by ASME
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