Stochastic Response of Nonlinear Dynamic Systems Based on a Non-Gaussian Closure

[+] Author and Article Information
R. A. Ibrahim, A. Soundararajan, H. Heo

Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409

J. Appl. Mech 52(4), 965-970 (Dec 01, 1985) (6 pages) doi:10.1115/1.3169176 History: Received June 01, 1984; Revised December 01, 1984; Online July 21, 2009


The random response of nonlinear dynamic systems involving stochastic coefficients is examined. A non-Gaussian closure scheme is outlined and employed to resolve an observed contradiction of the results obtained by other techniques. The method is applied to a system possessing nonlinear damping. The stationary response is obtained by numerical integration of the closed differential equations of the moments (up to fourth order). An interesting feature of the numerical results reveals the existence of a jump in the response statistic functions. This new feature may be attributed to the fact that the non-Gaussian closure more adequately models the nonlinearity, and thus results in characteristics that are similar to those of deterministic nonlinear systems. The results are compared with solutions derived by the Gaussian closure and stochastic averaging method.

Copyright © 1985 by ASME
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