Title

On Methods For Continuous Systems With Quadratic And Cubic Nonlinearities

Keywords

Averaged Lagrangian; Galerkin procedure; resonances; valve

Abstract

Methods for determining the response of continuous systems with quadratic and cubic nonlinearities are discussed. We show by means of a simple example that perturbation and computational methods based on first discretizing the systems may lead to erroncous results whereas perturbation methods that attack directly the nonlinear partial-differential equations and boundary conditions avoid the pitfalls associated with the analysis of the discretized systems. We describe a perturbation technique that applies either the method of multiple scales or the method of averaging to the Lagrangian of the system rather than the partial-differential equations and boundary conditions. © 1992 Kluwer Academic Publishers.

Publication Date

3-1-1992

Publication Title

Nonlinear Dynamics

Volume

3

Issue

2

Number of Pages

145-162

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF00118990

Socpus ID

0000301924 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0000301924

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