Global Bifurcations and Multi-Pulse Chaotic Dynamics of a Rectangular Thin Plate With One-to-One Internal Resonance

LI Shuang-bao; ZHANG Wei

doi:10.3879/j.issn.1000-0887.2012.09.002

Volume 33 Issue 9

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LI Shuang-bao, ZHANG Wei. Global Bifurcations and Multi-Pulse Chaotic Dynamics of a Rectangular Thin Plate With One-to-One Internal Resonance[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1043-1055. doi: 10.3879/j.issn.1000-0887.2012.09.002

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Global Bifurcations and Multi-Pulse Chaotic Dynamics of a Rectangular Thin Plate With One-to-One Internal Resonance

doi: 10.3879/j.issn.1000-0887.2012.09.002

LI Shuang-bao^1
,,
ZHANG Wei²

¹College of Science, Civil Aviation University of China, Tianjin 300300, P.R.China;²College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P.R.China

Received Date: 2011-07-20
Rev Recd Date: 2012-05-06
Publish Date: 2012-09-15

Abstract

Abstract

Global bifurcations and multipulse chaotic dynamics for a simply supported rectangular thin plate were studied using the extended Melnikov method for the first time. The rectangular thin plate was subjected to transversal and inplane excitations. A two-degree-of-freedom nonlinear non-autonomous system governing equations of motion for the rectangular thin plate was derived using the von Karman type equation and the Galerkin’s approach. The resonant case considered here is 1∶1 internal resonance. The averaged equation was obtained by the method of multiple scales. After transforming the averaged equation into a standard form, the extended Melnikov method was employed to show the existence of multi-pulse chaotic dynamics, which coudle be applied to explain the mechanism of modal interactions of thin plates. A skill for calculating the Melnikov function was given without the explicit analytical expression of homoclinic orbits. Furthermore, the restrictions on the damping, excitations and the detuning parameters were obtained, under which multi-pulse chaotic dynamics was expected. The results of numerical simulations are also given to indicate the existence of small amplitude multipulse chaotic responses for the rectangular thin plate.
- rectangular thin plate,
- global bifurcations,
- multi-pulse chaotic dynamics,
- extended Melnikov method

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References(23)

References

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