Free vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis

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Abstract


The aim of the work. Free, transverse vibrations are considered heterogeneous along the three spatial coordinates of rectangular plates lying on an inhomogeneous viscoelastic base. It is assumed that the boundary conditions are homogeneous. A closed solution for the problem of free vibration of an inhomogeneous rectangular orthotropic plate based on an inhomogeneous viscoelastic foundation is developed in the article. Young's moduli and the density of the orthotropic plate continuously change with respect to three spatial coordinates, while the characteristics of a viscoelastic base change depending on the coordinates in the plane. Methods. The corresponding equation of motion is obtained using the classical theory of plates. The solution to the problem was constructed using the method of separation of variables and the Bubnov - Galerkin method. Results. Explicit formulas of the fundamental tone of the frequency of the transverse vibration of an anisotropic plate lying on an inhomogeneous viscoelastic base are determined. The influence of heterogeneity of orthotropic materials, viscosity inhomogeneities, inelastic and elastic substrates at dimensionless plate frequencies have been studied in detail.


About the authors

Vaqif C. Haciyev

National Academy of Sciences of Azerbaijan

Author for correspondence.
Email: gulnar.mirzayeva@gmail.com
9 B. Wahabzadeh St., Baku, АZ1143, Republic of Azerbaijan

Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics

Gulnar R. Mirzoeva

National Academy of Sciences of Azerbaijan

Email: gulnar.mirzayeva@gmail.com
9 B. Wahabzadeh St., Baku, АZ1143, Republic of Azerbaijan

Doctor of Philosophy in Mechanics, senior researcher of Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics.

Matlab G. Agayarov

Sumgait State University

Email: gulnar.mirzayeva@gmail.com
43 quarter, Sumgait, AZ50008, Republic of Azerbaijan

Doctor of Philosophy in Mathematics and Mechanics Sciences, Associate Professor, Head of Additional Education Center

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Copyright (c) 2019 Haciyev V.C., Mirzoeva G.R., Agayarov M.G.

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