1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities

CHEN Yu-shu; YANG Cai-xia; WU Zhi-qiang; CHEN Fang-qi

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(8): 817-824

CHEN Yu-shu, YANG Cai-xia, WU Zhi-qiang, CHEN Fang-qi. 1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 2001, 22(8): 817-824.

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1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities

Department of Mechanics, Tianjin University, Tianjin 300072, P R China

Received Date: 2000-05-08
Rev Recd Date: 2001-03-15
Publish Date: 2001-08-15

Abstract

Abstract

The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied.The normal forms of this system in 1:2 internal resonance were derived by using the direct method of normal form.In the normal forms,quadratic and cubic nonlinearities were remained.Based on a new convenient transformation technique,the 4-dimension bifurcation equations were reduced to 3-dimension.A bifurcation equation with one-dimension was obtained.Then the bi furcation behaviors of a universal unfolding were studied by using the singularity theory.The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.
- quadratic and cubic nonlinearities,
- Normal Form,
- 1:2 internal resonance

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References(13)

References

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