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�������պ����ѧѧ�� 1998, Vol. 24 Issue (5) :592-595    DOI:
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Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System
Gan Chunbiao, Lu Qishao, Huang Kelei*
Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics

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ժҪ ��ģ̬�ķ���������һ�����е��������ķ��������Van der Pol����ϵͳ,�о��˴�ϵͳ�ķ�����ģ̬�˶����ֲ�,��ͨ�����ۺ���ֵ�����ģ̬�˶����ȶ��Ժͺϳ��Խ����˷���.�о��������,ģ̬�ĺϳ�����Ч��ģ��ԭϵͳ��˥��ЧӦ,����ϵͳ��˥���˶�ʱ,���ۺ���ֵ���֮�������С.Ȼ��,��ϵͳ�IJ�����Խij��ֵ��,ϵͳ��ģ̬�˶����̷���Hopf�ֲ�,����һ���ȶ��ļ��޻�,��ʱ,ģ̬�ĺϳ�ʧЧ,�ر��������λ��.
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Abstract�� This paper deals with a coupled nonlinear Van der Pol oscillator system with linear coupled elastic term,the dissimilar modes and their bifurcations have been discussed by modal analysis.Moreover,the stabilities and the superposition of the dissimilar modes have also been analyzed theoretically and numerically.It is shown that the modal superposition can effectively simulate the system's attenuation effects,the theoretical results are compared with the numerical ones,it is found that there exit very small errors between each other.However,when the parameter of the system passes through some value,the Hopf bifurcation takes place and a stable limit cycle arises in the modal equation of the system,and as a result,the modal superposition lose its efficacy,especially in their phase positions.
Keywords�� nonlinear   stability   synthesis   nonconservative   modal bifurcation     
Received 1997-10-07;
Fund:

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�ʴ���, ½����, �ƿ���.�����ԷDZ������ϵͳ��ģ̬�ֲ����ȶ���[J]  �������պ����ѧѧ��, 1998,V24(5): 592-595
Gan Chunbiao, Lu Qishao, Huang Kelei.Modal Bifurcations and Stability Analysis of a Nonconservative Nonlinear Coupled System[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 1998,V24(5): 592-595
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