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Finite element analysis of nonlinear oscillators
Author(s) -
Krishnamurthy K.,
Burton Thomas D.,
Zeller Lavern D.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210303
Subject(s) - subharmonic function , finite element method , nonlinear system , mathematical analysis , mathematics , element (criminal law) , boundary value problem , function (biology) , physics , quantum mechanics , law , evolutionary biology , biology , political science , thermodynamics
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 + ϵ f (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 + ϵ f (u) = P sin Ωt, is also considered, and it is shown that the superharmonic response can be efficiently calculated using this technique.