ISSN:
1573-269X
Keywords:
Averaged Lagrangian
;
valve
;
resonances
;
Galerkin procedure
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00118990
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