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Free Vibrations of a Transversely Isotropic Plate with Application to a Multilayer Nano-Plate

  • Nikita F. Morozov
  • Petr E. Tovstik
  • Tatyana P. Tovstik
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 46)

Abstract

Free vibrations of a transversely isotropic rectangular plate are investigated with the help of the Timoshenko–Reissner (TR) model including a transversal shear. The dependence of the principal natural frequency on the shear parameter for various variants of boundary conditions is found. The generalized Kirchhoff–Love (GKL) model of fourth differential order for a multilayered plate is proposed. The GKL model is simpler than the TR model, and in the most cases it gives the same results as the TR model. This model is used to describe vibrations of multilayer graphene sheets (MLGS). Explicit formulas for principal frequencies for both multilayer ordinary plates and for MLGS.

Keywords

Multilayer plate Free vibrations Generalized Kirchhoff-Love model Boundary conditions effect Multilayer graphene plate vibration 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nikita F. Morozov
    • 1
  • Petr E. Tovstik
    • 1
  • Tatyana P. Tovstik
    • 2
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical Engineering RASSt. PetersburgRussia

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