Spectral Approach to Equivalent Statistical Quadratization and Cubicization Methods for Nonlinear Oscillators
Publication: Journal of Engineering Mechanics
Volume 129, Issue 1
Abstract
Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian response. By using these expressions, statistics of the response are determined using the statistics of the Fourier coefficients of the first-order response, which can be readily computed since these coefficients are independent zero-mean Gaussian variables. In this manner, a significant reduction of the computational cost is achieved, as compared to alternative formulations of quadratization and cubicization methods where rather prohibitive multifold integrals in the frequency domain must be determined. Illustrative examples demonstrate the reliability of the proposed technique by comparison with data from pertinent Monte Carlo simulations.
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Published In
Journal of Engineering Mechanics
Volume 129 • Issue 1 • January 2003
Pages: 31 - 42
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Apr 11, 2002
Accepted: Apr 11, 2002
Published online: Dec 13, 2002
Published in print: Jan 2003
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