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Dynamical analysis of axially moving plate by finite difference method

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Abstract

The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.

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Authors and Affiliations

  1. Department of Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang, 110136, China

    Xiao-Dong Yang

  2. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100022, China

    Wei Zhang & Ming-Hui Yao

  3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai, 200072, China

    Li-Qun Chen

  4. Department of Mechanics, Shanghai University, Shanghai, 200444, China

    Li-Qun Chen

Authors
  1. Xiao-Dong Yang
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  2. Wei Zhang
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  3. Li-Qun Chen
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  4. Ming-Hui Yao
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Correspondence to Wei Zhang.

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Yang, XD., Zhang, W., Chen, LQ. et al. Dynamical analysis of axially moving plate by finite difference method. Nonlinear Dyn 67, 997–1006 (2012). https://doi.org/10.1007/s11071-011-0042-2

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  • DOI: https://doi.org/10.1007/s11071-011-0042-2

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