Technical Briefs

Nonclassical Linearization Criteria in Nonlinear Stochastic Dynamics

[+] Author and Article Information
Isaac Elishakoff

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991

Lova Andriamasy

 French Institute For Advanced Mechanics (IFMA), Clermont-Ferrand, 63175 Aubière Cedex, France

J. Appl. Mech 77(4), 044501 (Mar 25, 2010) (5 pages) doi:10.1115/1.4000899 History: Received January 10, 2008; Revised April 13, 2009; Published March 25, 2010; Online March 25, 2010

In classical stochastic linearization method, the nonlinear force is replaced by an equivalent linear one. Several nonclassical schemes were suggested in recent years, based on potential or complementary energy criteria. Here, these criteria are compared with each other, and the classical stochastic linearization scheme, to determine their efficacy.

Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Comparison of the approximate solutions with the exact results: (1) exact solution; (2) potential energy criterion in Eq. 10; and (3) classical stochastic linearization results

Grahic Jump Location
Figure 2

Contrast of the potential and complementary energy criteria with the exact solution: a—exact solution; b—criterion based on equality of mean-squares of potential energies in Eq. 27; c—criterion based on complementary energy in Eq. 13; and d—criterion based on equality of mean-squares of complementary energies



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