SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (10): 1122-1133.

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

李欣业, 陈予恕, 吴志强

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

收稿日期:2001-05-08 修回日期:2002-05-10 出版日期:2002-10-18 发布日期:2002-10-18
基金资助:
the National Natural Science Foundation of China(19990510);the National Key Basic Research Special Foundation of China(G1998020316);the Doctoral Point Foundation of Education Ministry

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang

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

Received:2001-05-08 Revised:2002-05-10 Online:2002-10-18 Published:2002-10-18
Supported by:
the National Natural Science Foundation of China(19990510);the National Key Basic Research Special Foundation of China(G1998020316);the Doctoral Point Foundation of Education Ministry

摘要/Abstract

摘要： The nonlinear normal modes(NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of systems with 1:2:5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

关键词: dual internal resonance, nonlinear normal mode, mode coupling, mode bifurcation, the singularity theory

Abstract: The nonlinear normal modes(NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of systems with 1:2:5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

Key words: dual internal resonance, nonlinear normal mode, mode coupling, mode bifurcation, the singularity theory

中图分类号:

O322

李欣业;陈予恕;吴志强. SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1122-1133.

LI Xin-ye;CHEN Yu-shu;WU Zhi-qiang . SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1122-1133.

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SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

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