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- Title
1:2 Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities.
- Authors
Chen, Yu-shu; Yang, Cai-xia; Wu, Zhi-qiang; Chen, Fang-qi
- 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 bifurcation 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.
- Subjects
HYBRID systems; BIFURCATION theory; NORMAL forms (Mathematics); LAGRANGE equations; NONLINEAR statistical models; RESONANCE
- Publication
Applied Mathematics & Mechanics, 2001, Vol 22, Issue 8, p917
- ISSN
0253-4827
- Publication type
Article
- DOI
10.1023/A:1016342326645