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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses

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Contributions to Advanced Dynamics and Continuum Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 114))

Abstract

We discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only on the density distribution in the bulk but also on the surface mass density.

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Acknowledgements

The second author acknowledges financial support from the Russian Science Foundation under the grant “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No 15-19-10008-P).

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Authors and Affiliations

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

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, ul. Gabriela Narutowicza 11/12, 80-233, Gdańsk, Poland

    Victor A. Eremeyev

  3. Southern Federal University, Milchakova str. 8a, 344090, Rostov on Don, Russia

    Victor A. Eremeyev

  4. Southern Scientific Center of RASci, Chekhova str. 41, 344006, Rostov on Don, Russia

    Victor A. Eremeyev

Authors
  1. Holm Altenbach
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  2. Victor A. Eremeyev
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Correspondence to Victor A. Eremeyev .

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Editors and Affiliations

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

    Holm Altenbach

  2. Institut für Technische Mechanik, Johannes Kepler Universität Linz, Linz, Austria

    Hans Irschik

  3. Institute of Continuous Media Mechanics, Russian Academy of Sciences, Perm, Russia

    Valery P. Matveenko

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Altenbach, H., Eremeyev, V.A. (2019). On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses. In: Altenbach, H., Irschik, H., Matveenko, V. (eds) Contributions to Advanced Dynamics and Continuum Mechanics. Advanced Structured Materials, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-030-21251-3_2

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