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Stability and bifurcation of a cantilever functionally graded material plate subjected to the transversal excitation

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Abstract

The stability and bifurcation behaviors for a cantilever functionally graded materials rectangular plate subjected to the transversal excitation in thermal environment are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1:1 internal resonances and 1/2 subharmonic resonance. Four types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, a double zero and a pair of pure imaginary eigenvalues, a simple zero and a pair of pure imaginary eigenvalues as well as two pairs of pure imaginary eigenvalues in non-resonant case, respectively. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained, which may lead to static bifurcation and Hopf bifurcation. The numerical solutions obtained by using fourth-order Runge-Kutta method agree with the analytic predictions.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (11172125), and the National Research Foundation for the Doctoral Program of Higher Education of China (20133218110025).

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Authors and Affiliations

  1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Dongmei Zhang

  2. School of Science, Linyi University, Shandong, 276005, People’s Republic of China

    Dongmei Zhang

  3. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Fangqi Chen

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  1. Dongmei Zhang
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  2. Fangqi Chen
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Correspondence to Dongmei Zhang.

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Zhang, D., Chen, F. Stability and bifurcation of a cantilever functionally graded material plate subjected to the transversal excitation. Meccanica 50, 1403–1418 (2015). https://doi.org/10.1007/s11012-015-0101-8

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  • DOI: https://doi.org/10.1007/s11012-015-0101-8

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