Finite Element Analysis of Nonlinear Oscillators

Abstract

Presented in this paper is a finite element method for the analysis of nonlinear oscillations which exhibit periodic response. The basic idea of the method is to recast the initial value problem as a boundary value problem in which the domain (that is, period) may be unknown. We apply the method to study the free response of the conservative oscillator ü + mu + ϵf(u)=0, where m is either − 1, 0 or 1, f(u) is an odd nonlinear function, and ϵ need not be small. The harmonically forced case, ü + mu + ϵf(u) = Psin Ωt, is also considered, and it is shown that the superharmonic response can be efficiently calculated using this technique.

Department(s)

Mechanical and Aerospace Engineering

Keywords and Phrases

Mathematical Techniques - Finite Element Method; Nonlinear Oscillators; Superharmonic Responses; Vibrators

International Standard Serial Number (ISSN)

0029-5981

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1985 John Wiley & Sons Ltd, All rights reserved.

Publication Date

01 Mar 1985

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