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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nayfeh A. H., Perturbation Methods, Wiley-Interscience, New York, 1973.
Nayfeh A. H., Introduction to Perturbation Techniques, Wiley-Interscience, New York, 1981.
Nayfeh A. H. and Bouguerra H., ‘Non-linear response of a fluid valve’, International Journal of Non-Linear Mechanics 25, 1990, 433–449.
Nayfeh A. H. and Mook D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.
Nayfeh A. H. ‘The response of single-degree-of-freedom systems with quadratic and cubic nonlinearities to a subharmonic excitation’, Journal of Sound and Vibration 89, 1983, 457–470.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nayfeh, A.H., Nayfeh, J.F. & Mook, D.T. On methods for continuous systems with quadratic and cubic nonlinearities. Nonlinear Dyn 3, 145–162 (1992). https://doi.org/10.1007/BF00118990
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00118990