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Bifurcation and chaos of the circular plates on the nonlinear elastic foundation

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Abstract

According to the large amplitude equation of the circular plate on nonlinear elastic foundation, elastic resisting force has linear item, cubic nonlinear item and resisting bend elastic item. A nonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary. Floquet exponent at equilibrium point is obtained without external excitation. Its stability and condition of possible bifurcation is analysed. Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation. The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.

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Authors and Affiliations

  1. School of Science, Lanzhou University of Science and Technology, 730050, Lanzhou, PR China

    Qiu Ping & Wang Xin-zhi

  2. Physics College, Lanzhou University, 730000, Lanzhou, PR China

    Yeh Kai-yuan

Authors
  1. Qiu Ping
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  2. Wang Xin-zhi
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  3. Yeh Kai-yuan
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Additional information

Contributed by YEH Kai-yuan

Foundation item: the Natural Science Foundation of Gansu Province (ZS021-A25-007-Z)

Biography: QIU Ping (1954∼), Associate Professor (E-mail: qiup@gsut.edu.cn)

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Ping, Q., Xin-zhi, W. & Kai-yuan, Y. Bifurcation and chaos of the circular plates on the nonlinear elastic foundation. Appl Math Mech 24, 880–885 (2003). https://doi.org/10.1007/BF02446492

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  • DOI: https://doi.org/10.1007/BF02446492

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Chinese Library Classification

2000 Mathematics Subject Classification

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