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Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation

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Abstract

The global bifurcations in mode interaction of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation are investigated with the case of the 1:1 internal resonance, the average equations representing the evolution of the amplitudes and phases of the interacting normal modes exhibiting complex dynamics. A global perturbation method, i.e., the higher-dimensional Melnikov method and its extensions proposed by Kovačič and Wiggins, is utilized to analyze the global bifurcations for the rectangular metallic plate. A sufficient condition for the existence of a Silnikov-type homoclinic orbit is obtained, which implies that chaotic motions may occur for this class of rectangular metallic plates. Finally, numerical results are presented to confirm these analytical predictions.

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  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, PR China

    Weiqin Yu & Fangqi Chen

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  1. Weiqin Yu
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  2. Fangqi Chen
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Correspondence to Weiqin Yu.

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Yu, W., Chen, F. Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation. Nonlinear Dyn 59, 129–141 (2010). https://doi.org/10.1007/s11071-009-9526-8

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