Abstract
The authors of [1] discussed the subharmonic resonance bifurcation theory of nonlinear Mathieu equation and obtained six bifurcation diagrams in (α,β) -plane. In this paper, we extended the results of [1] and pointed out that there may exist as many as fourteen bifurcation diagrams which are not topologically equivalent to each other.
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References
Chen Yu-shu and W. F. Langford, The subharmonic bifurcation solution of nonlinear mathieu equation and euler dynamic buckling problems,Acta Mechanica Sinica,4, 4 (1988). (in Chinese)
Golubitsky, M. and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol.1, Springer-Verlag (1985).
Chen Yu-shu, Zhou Kai-jun and W. F. Langford, Degenerate bifurcation of one Nonlinear and Parametric vibration system (submitted toJ. Vibration Engineering). (in Chinese)
Chen Yu-shu, Wu Jiang-guo and Jin Zhi-sheng, Bifurcation problem of parametrically excited torsional vibration of crankshaft system,J. of Vib. Eng., 1 (1987). (in Chinese)
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Communicated by Zhou Heng
Supported by the National Natural Science Foundation of China.
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Yu-shu, C., Kai-jun, Z. Some extended results of “subharmonic resonance bifurcation theory of nonlinear Mathieu equation”. Appl Math Mech 11, 255–261 (1990). https://doi.org/10.1007/BF02015206
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DOI: https://doi.org/10.1007/BF02015206