| SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES |
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| 作者姓名： | 李欣业 陈予恕 吴志强 |
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| 作者单位： | LI Xin_ye，CHEN Yu_shu，WU Zhi_qiang (Department of Mechanics，Tianjin University，Tianjin 300072，P R China) (Contributed by CHEN Yu_shu) |
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| 基金项目： | theNationalNaturalScienceFoundationofChina ( 1 9990 51 0 )，theNationalKeyBasicResearchSpecialFoundationofChina (G1 9980 2 0 3 1 6)，theDoctoralPointFoundationofEducationMinistry |
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| 摘 要： | ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｉｎｔｅｒｅｓｔｉｎｇｆｅａｔｕｒｅｉｎｔｈｅｆｒｅｅｖｉｂｒａｔｉｏｎｏｆａｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｉｓｔｈｅｆａｃｔｔｈａｔｔｈｅｎｕｍｂｅｒｏｆｅｘｉｓｔｉｎｇｎｏｒｍａｌｍｏｄｅｓｍａｙｅｘｃｅｅｄｔｈｅｎｕｍｂｅｒｏｆｄｅｇｒｅｅｓｏｆｆｒｅｅｄｏｍ ,ａｐｈｅｎｏｍｅｎｏｎｎｏｔｅｎｃｏｕｎｔｅｒｅｄｉｎａｌｉｎｅａｒｓｙｓｔｅｍａｎｄｃａｕｓｅｄｂｙｍｏｄｅｂｉｆｕｒｃａｔｉｏｎ .Ｔｈｅｒｅｆｏｒｅｍｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｏｎｅｏｎｔｈｅｓｔ…
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| 收稿时间： | 8 May 2001 |
Singular analysis of bifurcation of nonlinear normal modes for a class of systems with dual internal resonances |
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| Li Xin-ye Associate Professor, Doctor,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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| Authors: | Li Xin-ye Associate Professor Doctor Chen Yu-shu Wu Zhi-qiang |
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| Institution: | Department of Mechanics, Tianjin University, Tianjin 300072, P R China |
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| 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
paterns 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 degress 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.
Contributed by CHEN Yu-shu
Foundation items: 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
Biography: LI Xin-ye (1996−) |
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| Keywords: | dual internal resonance nonlinear normal mode mode coupling mode bifurcation the singularity theory |
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