Multi-pulse jumping orbits and homoclinic trees in motion of a simply supported rectangular metallic plate |
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Authors: | Weiqin Yu Fangqi Chen |
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Institution: | 1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China 2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China
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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 modulation equations representing the evolution
of the amplitudes and phases of the interacting normal modes exhibit complex dynamics. The energy-phase method proposed by
Haller and Wiggins is employed to analyze the global bifurcations for the rectangular metallic plate. The results obtained
here indicate that there exist the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the resonant
case in both Hamiltonian and dissipative perturbations, which imply that chaotic motions may occur for this class of systems.
Homoclinic trees which describe the repeated bifurcations of multi-pulse solutions are found. To illustrate the theoretical
predictions, we present visualizations of these complicated structures and numerical evidence of chaotic motions. |
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Keywords: | |
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