MATEC Web of Conferences
Volume 45, 20162016 7th International Conference on Mechatronics and Manufacturing (ICMM 2016)
|Number of page(s)||5|
|Section||Power Machine and Engineering|
|Published online||15 March 2016|
Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System
1 Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, 100124, China
2 Beijing University of Technology, College of Mechanical Engineering, 100124, China
In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems. As an example, we investigate the multi-pulse orbits and homoclinic trees for a parametrically excited, simply supported rectangular thin plate of two-mode approximation. In both the Hamiltonian and dissipative case we find homoclinic trees, which describe the repeated bifurcations of multi-pulse solutions, and we present visualizations of these complicated structures.
© Owned by the authors, published by EDP Sciences, 2016
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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