On the Vibrations of a Simply Supported Square Plate on a Weakly Nonlinear Elastic Foundation |
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Authors: | M?A?Zarubinskaya Email author" target="_blank">W?T?van?HorssenEmail author |
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Institution: | (1) Department of Applied Mathematical Analysis, Faculty of Information Technology and Systems, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands |
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Abstract: | In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is assumed that the foundation has a different behavior for compression and for expansion. An approximation for the solution of the initial-boundary value problem will be constructed using a two-timescales perturbation method. The existence and uniqueness of the solution of the problem will be proved. Also the asymptotic validity of the constructed approximations will be shown on long timescales. For specific parameter values, it turns out that complicated internal resonances occur. |
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Keywords: | asymptotics internal resonances two-timescales perturbation method weakly nonlinear plate equation |
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