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A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Plate with 2:1 and 2:1:1 Internal Resonances

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Shell and Membrane Theories in Mechanics and Biology

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 45))

Abstract

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the internal resonances two-to-one and one-to-one, as well as the internal combinational resonances has been studied by Rossikhin and Shitikova in [12, 13]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to solve the problems of vibrations of thin bodies more efficiently.

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Acknowledgments

The research described in this publication has been supported by the Russian Ministry of High Education and Science. (No 7.22.2014/K)

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Authors and Affiliations

  1. Research Center of Wave Dynamics, Voronezh State University of Architecture and Civil Engineering, Voronezh, 394006, Russia

    Yury A. Rossikhin & Marina V. Shitikova

Authors
  1. Yury A. Rossikhin
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  2. Marina V. Shitikova
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Correspondence to Yury A. Rossikhin .

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Editors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Department of Bio- and Nanomechanics, Belarusian State University, Minsk, Belarus

    Gennadi I. Mikhasev

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Rossikhin, Y.A., Shitikova, M.V. (2015). A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Plate with 2:1 and 2:1:1 Internal Resonances. In: Altenbach, H., Mikhasev, G. (eds) Shell and Membrane Theories in Mechanics and Biology. Advanced Structured Materials, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-02535-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-02535-3_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02534-6

  • Online ISBN: 978-3-319-02535-3

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