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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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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.

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Authors and Affiliations

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

    Li Xin-ye Associate Professor, Doctor, Chen Yu-shu & Wu Zhi-qiang

Authors
  1. Li Xin-ye Associate Professor, Doctor
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  2. Chen Yu-shu
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  3. Wu Zhi-qiang
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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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Xin-ye, L., Yu-shu, C. & Zhi-qiang, W. Singular analysis of bifurcation of nonlinear normal modes for a class of systems with dual internal resonances. Appl Math Mech 23, 1122–1133 (2002). https://doi.org/10.1007/BF02437660

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  • DOI: https://doi.org/10.1007/BF02437660

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