Abstract
The1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in1:2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the4-dimension bifurcation equations were reduced to3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on4-dimension center manifolds.
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Paper from Chen Yu-shu, Member of Editorial Commuttee, AMM
Foundation item: the National Natural Science Foundation of China (1990510); the National Key Basic Research Special Fund (G1998020316); the Doctoral Point Fund of Education Committee of China (D09901)
Biography: Chen Yu-shu (1931-)
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Yu-shu, C., Cai-xia, Y., Zhi-qiang, W. et al. 1:2 Internal resonance of coupled dynamic system with quadratic and cubic nonlinearities. Appl Math Mech 22, 917–924 (2001). https://doi.org/10.1007/BF02436390
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DOI: https://doi.org/10.1007/BF02436390