Stochastic linearization technique: A new interpretation and a selective review

Author Type

Faculty

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Shock and Vibration Digest

Publication Status

Version of Record

Abstract

Several developments in stochastic linearization are summarized in this review paper, along with the new, statistical orthogonality-based derivation of the method. A nonlinear oscillator subjected to colored noise is examined, the case of nonlinear damping is discussed, and the `true' stochastic linearization technique is described. The results of the latter match the exact mean square responses of a nonlinear structure. A combination of stochastic linearization with the Monte Carlo method is outlined. In addition, the accuracy of an energy linearization technique versus the newly interpreted classical scheme is examined for a Duffing oscillator subjected to white or colored noise excitations. The results obtained by the two schemes are compared in terms of percentage-wise error relative to the exact solution or relative to numerical results obtained through Monte Carlo simulation. These applications confirm the superiority of the energy linearization technique over the force linearization technique in several examples considered. In certain circumstances, however, namely for some nonlinear softening oscillators, newly interpreted conventional linearization may yield more accurate results. The method of weighing functions improves the accuracy of both methods.

First Page

179

Last Page

188

DOI

10.1177/058310240003200301

Publication Date

1-1-2000

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