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On Mode Interactions for a Weakly Nonlinear Beam Equation
Authors:Boertjens  G J  Van Horssen  W T
Institution:(1) Department of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
Abstract:In this paper an initial-boundary value problem for a weakly nonlinear beam equation with a Rayleigh perturbation will be studied. It will be shown that the calculations to find internal resonances in this case are much more complicated than and differ substantially from the calculations for the weakly nonlinear wave equation with a Rayleigh perturbation as for instance presented in 3] or 7]. The initial-boundary value problem can be regarded as a simple model describing wind-induced oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-timescales perturbation method approximations for solutions of this initial-boundary value problem will be constructed.
Keywords:Weakly nonlinear beam equation  Galerkin mode truncation  two-timescales perturbation method  internal resonances
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