Finite Element Analysis of Nonlinear Oscillators
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.
K. Krishnamurthy et al., "Finite Element Analysis of Nonlinear Oscillators," International Journal for Numerical Methods in Engineering, vol. 21, no. 3, pp. 409-420, John Wiley & Sons Ltd, Mar 1985.
The definitive version is available at https://doi.org/10.1002/nme.1620210303
Mechanical and Aerospace Engineering
Keywords and Phrases
Mathematical Techniques - Finite Element Method; Nonlinear Oscillators; Superharmonic Responses; Vibrators
International Standard Serial Number (ISSN)
Article - Journal
© 1985 John Wiley & Sons Ltd, All rights reserved.