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Free vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis
- Authors: Haciyev V.C.1, Mirzoeva G.R.1, Agayarov M.G.2
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Affiliations:
- National Academy of Sciences of Azerbaijan
- Sumgait State University
- Issue: Vol 15, No 6 (2019)
- Pages: 470-476
- Section: Dynamics of structures and buildings
- URL: https://journals.rudn.ru/structural-mechanics/article/view/22573
- DOI: https://doi.org/10.22363/1815-5235-2019-15-6-470-476
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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.
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About the authors
Vaqif C. Haciyev
National Academy of Sciences of Azerbaijan
Author for correspondence.
Email: gulnar.mirzayeva@gmail.com
Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics
9 B. Wahabzadeh St., Baku, АZ1143, Republic of AzerbaijanGulnar R. Mirzoeva
National Academy of Sciences of Azerbaijan
Email: gulnar.mirzayeva@gmail.com
Doctor of Philosophy in Mechanics, senior researcher of Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics.
9 B. Wahabzadeh St., Baku, АZ1143, Republic of AzerbaijanMatlab G. Agayarov
Sumgait State University
Email: gulnar.mirzayeva@gmail.com
Doctor of Philosophy in Mathematics and Mechanics Sciences, Associate Professor, Head of Additional Education Center
43 quarter, Sumgait, AZ50008, Republic of AzerbaijanReferences
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