ON THE ERGODICITY ASSUMPTION IN APPLIED MECHANICS.

Author Type

Outside Researcher

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

Conference Proceeding

Publication Status

Version of Record

Abstract

A variety of problems in structural mechanics are governed by random nonlinear differential equations, for which exact solutions are unavailable, and approximate solutions must be resorted to. The ergodicity assumption of the output is often utilized for obtaining probabilistic characteristics. An applied mechanics problem first studied by Bolotin is presented. Bolotin used the assumption to derive the second moment of the solution for the case of a white-noise input, and further showed that the first few terms of a perturbation solution were in agreement with the original result. An exact solution is given for Bolotin's problem. It is found that: a) the assumption of ergodicity of the output may yield a large error even for a mean-square ergodic input, b) this assumption is correct if the input is ergodic in correlation, and c) for an input which is ergodic in correlation, various probabilistic characteristics of the output are obtainable in terms of appropriate characteristics of the input.

First Page

284

Last Page

288

Publication Date

12-1-1984

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