Free vibrations of a transversely isotropic plate with application to a multilayer Nano-Plate

Nikita F. Morozov, Petr E. Tovstik, Tatyana Petrovna Tovstik

Research outputpeer-review

2 Citations (Scopus)

Abstract

Free vibrations of a transversely isotropic rectangular plate are investigated within the frameworks 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 it gives the same results as the TR model in the most cases. 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 are derived.

Original languageEnglish
Title of host publicationAdvanced Structured Materials
PublisherSpringer
Pages349-362
Number of pages14
Volume46
DOIs
Publication statusPublished - 2017

Publication series

NameAdvanced Structured Materials
Volume46
ISSN (Print)1869-8433
ISSN (Electronic)1869-8441

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Scopus subject areas

  • Materials Science(all)

Cite this

Morozov, N. F., Tovstik, P. E., & Tovstik, T. P. (2017). Free vibrations of a transversely isotropic plate with application to a multilayer Nano-Plate. In Advanced Structured Materials (Vol. 46, pp. 349-362). (Advanced Structured Materials; Vol. 46). Springer. https://doi.org/10.1007/978-3-319-56050-2_20