Methods and Gaussian Criterion for Statistical Linearization of Stochastic Parametrically and Externally Excited Nonlinear Systems

[+] Author and Article Information
R. J. Chang

Department of Mechanical Engineering, National Chong Kung University, Tainan, Taiwan 70101

G. E. Young

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078

J. Appl. Mech 56(1), 179-185 (Mar 01, 1989) (7 pages) doi:10.1115/1.3176042 History: Received June 23, 1987; Revised April 05, 1988; Online July 21, 2009


The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented. The techniques of Gaussian linearization are first derived and the accuracy in the prediction of the stationary output variances is illustrated. The justification of using Gaussian linearization a priori is further investigated by establishing a Gaussian Criterion. The non-Gaussian effects due to system nonlinearities and/or large noise intensities in a Duffing oscillator are also illustrated. The validity of employing the Gaussian Criterion test for assuring accuracy of Gaussian linearization is supported by performing the Chi-square Gaussian goodness-of-fit test.

Copyright © 1989 by ASME
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