Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

被引：6
|
作者：
Shi Pei-Ming [1 ]
Liu Bin [1 ]
Jiang Jin-Shui [1 ]
机构：
[1] Yanshan Univ, Measurement Technol & Instrumentat Key Lab Hebei, Qinhuangdao 066004, Peoples R China
来源：
ACTA PHYSICA SINICA | 2009年 / 58卷 / 04期
关键词：
relative rotation; nonlinear coupling dynamic system; singularity theory; stability; EQUILIBRIUM STATE; TORSIONAL SYSTEM; LIE SYMMETRIES; POISSON INTEGRALS; FORM INVARIANCE; EQUATIONS; MOTION; QUANTITIES; VIBRATION; MECHANICS;
D O I：
10.7498/aps.58.2147
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The dynamic behaviors of a relative-rotation nonlinear dynamic system with cubic coupled terms are studied. First, the dynamic equation of coupled system with nonlinear elastic force and generalized friction and harmonic excitation is deduced. The approximate solution of coupled unautonomous equation under harmonic excitation is obtained by the method of multiple scales. The effect of coupled terms on system resonance is analyzed in respect of principal resonance and internal resonance. The singularity stability of bifurcation function of principal resonance is studied by singularity theory, and the transfer concourse and topological structure of bifurcation function are obtained.
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页码：2147 / 2154
页数：8
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