On methods for continuous systems with quadratic and cubic nonlinearities

✍ Scribed by A. H. Nayfeh; J. F. Nayfeh; D. T. Mook

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 737 KB
• Volume: 3
• Category: Article
• ISSN: 0924-090X
• DOI: 10.1007/bf00118990

✦ Synopsis

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 erroneous results whereas perturbation methods that attack directly the nonlinear partialdifferential 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.