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Global bifurcations and homoclinic trees in motion of a thin rectangular plate on a nonlinear elastic foundation

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Abstract

The global bifurcations and chaotic dynamics of a thin rectangular plate on a nonlinear elastic foundation subjected to a harmonic excitation are investigated. On the basis of the amplitude and phase modulation equations derived by the method of multiple scales, a near integrable two-degree-of-freedom Hamiltonian system is obtained by a transformation. The energy-phase method proposed by Haller and Wiggins is employed to analyze the global bifurcations for the thin rectangular plate. The results obtained here indicate that there exist the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the resonant case, which implies 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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Acknowledgements

The authors greatly appreciate the anonymous reviews for their insightful comments and suggestions for further improving the quality of this work. This work was supported by the National Nature Science Foundation of China (11202095, 11172125) and Shanghai Municipal Education Commission Research Foundation (shgcjs019).

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Authors and Affiliations

  1. Department of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, P.R. China

    Weiqin Yu

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China

    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 and homoclinic trees in motion of a thin rectangular plate on a nonlinear elastic foundation. Meccanica 48, 1251–1261 (2013). https://doi.org/10.1007/s11012-012-9665-8

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  • DOI: https://doi.org/10.1007/s11012-012-9665-8

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