1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (8): 917-924.

1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES

陈予恕, 杨彩霞, 吴志强, 陈芳启

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

收稿日期:2000-05-08 修回日期:2001-03-15 出版日期:2001-08-18 发布日期:2001-08-18
基金资助:
the National Natural Science Foundation of China(19990510);the National Key Basic Research Special Fund(G1998020316);the Doctoral Point Fund of Education Committee of China(D09901)

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

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

Received:2000-05-08 Revised:2001-03-15 Online:2001-08-18 Published:2001-08-18
Supported by:
the National Natural Science Foundation of China(19990510);the National Key Basic Research Special Fund(G1998020316);the Doctoral Point Fund of Education Committee of China(D09901)

摘要/Abstract

摘要： 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.

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.

中图分类号:

O193
O177.91

陈予恕;杨彩霞;吴志强;陈芳启. 1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(8): 917-924.

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 (English Edition), 2001, 22(8): 917-924.

参考文献

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1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES

1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES

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