Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique
type: Item
instance of: scholarly article
title: Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique
zbMATH Open document ID: 0874.73079
DOI: 10.1016/0020-7683(94)00198-6
author: Isaac Elishakoff
author: Jianjie Fang
author: Raoul Caimi
published in: International Journal of Solids and Structures
publication date: 1997-11-13T00:00:00Z
review text: A new stochastic linearization technique is employed to investigate the large amplitude random vibrations of a simply supported or a clamped beam on elastic foundation under a stochastic loading which is space-wise either (a) white noise or (b) uniformly distributed load and time-wise white noise. The new method is based on the requirement that the mean square deviation of the strain energy of the nonlinearly deformed beam, and the strain energy of the equivalent beam in a linear state, should be minimal. As a result, the model mean square displacements are expressed as solutions of a set of nonlinear algebraic equations. Results obtained by the conventional equivalent linearization method and by the new technique are compared with the numerical results obtained from integration of the exact probability density function or with the result of the Monte Carlo simulations.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 988965
zbMATH Keywords: large amplitude vibrations
zbMATH Keywords: clamped beam
zbMATH Keywords: elastic foundation
zbMATH Keywords: white noise
zbMATH Keywords: uniformly distributed load
zbMATH Keywords: strain energy
zbMATH Keywords: model mean square displacements
zbMATH Keywords: nonlinear algebraic equations
MaRDI profile type: Publication
full work available at URL: 0020-7683(94)00198-6
OpenAlex ID: W1985702870
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description: scientific article; zbMATH DE number 988965