Research Article
Aug 1975
Approximate Method for Nonlinear Random Vibration
Publication: Journal of the Engineering Mechanics Division
Volume 101, Issue 4
Abstract
An approximate method for nonstationary solution of nonlinear systems under random excitation is presented. The nonlinearities in the restoring force are polynomial type. The excitation is either shot noise or filtered shot noise. The solution is based on a Markov-vector approach. The unsteady Fokker-Planck-Kolmogorov equation for the nonlinear system is solved approximately by a Galerkin method where a time-dependent Hermite-series expansion is used and the equation is reduced to a system of first-order ordinary differential equations. The method is illustrated by numerical examples on a damped Duffing oscillator and a Ramsberg-Osgood yielding system. Comparison of results obtained herein with exact stationary solution and Monte Carlo results indicates that the proposed method is powerful and efficient for study of nonlinear systems.
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Published In
Journal of the Engineering Mechanics Division
Volume 101 • Issue 4 • August 1975
Pages: 389 - 401
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© 1975 American Society of Civil Engineers.
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Published in print: Aug 1975
Published online: Feb 3, 2021
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Yi-Kwei Wen, M.ASCE
Asst. Prof. of Civ. Engrg., Univ. of Illinois at Urbana-Champaign, Urbana, Ill.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.