1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES
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.
作 者： 陈予恕 杨彩霞 吴志强 陈芳启 作者单位： Department of Mechanics, Tianjin University, Tianjin 300072, P R China 刊 名： 应用数学和力学(英文版) EI SCI 英文刊名： APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION) 年，卷(期)： 2001 22(8) 分类号： O193 O177.91 关键词： quadratic and cubic nonlinearities Normal Form 1: 2 internal resonance