Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a honeycomb sandwich plate |
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Authors: | J H Zhang W Zhang |
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Affiliation: | 1.College of Mechanical Engineering,Beijing Information Science and Technology University,Beijing,People’s Republic of China;2.College of Mechanical Engineering,Beijing University of Technology,Beijing,People’s Republic of China |
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Abstract: | The global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under
combined parametric and transverse excitations are investigated in this paper for the first time. The extended Melnikov method
is generalized to investigate the multi-pulse chaotic dynamics of the non-autonomous nonlinear dynamical system. The main
theoretical results and the formulas are obtained for the extended Melnikov method of the non-autonomous nonlinear dynamical
system. The nonlinear governing equation of the honeycomb sandwich rectangular plate is derived by using the Hamilton’s principle
and the Galerkin’s approach. A two-degree-of-freedom non-autonomous nonlinear equation of motion is obtained. It is known
that the less simplification processes on the system will result in a better understanding of the behaviors of the multi-pulse
chaotic dynamics for high-dimensional nonlinear systems. Therefore, the extended Melnikov method of the non-autonomous nonlinear
dynamical system is directly utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the two-degree-of-freedom
non-autonomous nonlinear system for the honeycomb sandwich rectangular plate. The theoretical results obtained here indicate
that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Numerical simulation is also employed
to find the multi-pulse chaotic motions of the honeycomb sandwich rectangular plate. It also demonstrates the validation of
the theoretical prediction. |
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