A Parametrically Excited Nonlinear Wave Equation
Publication date
2020-11-03
Authors
Verhulst, Ferdinand
Tuwankotta, Johan M.
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Abstract
When considering nonlinear waves with periodic parametric forcing the geometry of the spatial domain plays a crucial part. If the spatial domain is a square we find an infinite number of 1 : 1 resonances and in addition accidental resonances. Using Galerkin projection on 2 modes in 1 : 1 resonance we find stable normal mode periodic solutions and unstable periodic solutions in general position; the location in phase-space is characterised as a triple resonance zone. In the limit case of vanishing dissipation we find neutral stability and strong recurrence of the orbits. Interaction of 1 : 1 resonances shows a selection mechanism of the 1 : 1 modes triggered off by the parametric forcing. In addition we analyse a number of prominent accidental resonances produced by the spectrum induced by our choice of a square in space.
Keywords
Taverne, General Materials Science
Citation
Verhulst, F & Tuwankotta, J M 2020, A Parametrically Excited Nonlinear Wave Equation. in Nonlinear Dynamics of Discrete and Continuous Systems. Advanced Structured Materials, vol. 139, Springer, pp. 155-169. https://doi.org/10.1007/978-3-030-53006-8_11