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.

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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

Abstract

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

2010 MSC Number:

O322

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. 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

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