Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)2257310.22363/1815-5235-2019-15-6-470-476Research ArticleFree vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basisHaciyevVaqif C.<p>Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics</p>gulnar.mirzayeva@gmail.comMirzoevaGulnar R.<p>Doctor of Philosophy in Mechanics, senior researcher of Department of Theory of Elasticity and Plasticity, Institute of Mathematics and Mechanics.</p>gulnar.mirzayeva@gmail.comAgayarovMatlab G.<p>Doctor of Philosophy in Mathematics and Mechanics Sciences, Associate Professor, Head of Additional Education Center</p>gulnar.mirzayeva@gmail.comNational Academy of Sciences of AzerbaijanSumgait State University1512201915647047629122019Copyright © 2019, Haciyev V.C., Mirzoeva G.R., Agayarov M.G.2019<p>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.</p>platecontinuityanisotropydensitybasesfrequencydeflectionequations of motionпластинканепрерывностьнеоднородностьанизотропностьплотностьоснованиячастотапрогибуравнения движения[Lomakin V.A. (1976). Teoriya uprugosti neodnorodnyh tel [The theory of elasticity of inhomogeneous walked]. Moscow, Publishing House of Moscow State University. (In Russ.)][Lehnitsky S.G. (1957). Anizotropnye plastinki [Anisotropic plates]. Gostekhizdat Publ. (In Russ.)][Kravchuk A.S., Mayboroda V.V., Urzhumtsev Yu.S. (1985). Mekhanika polimernyh i kompozicionnyh materialov [Mechanics of polymer and composite materials]. Moscow, Nauka Publ. (In Russ.)][Tornabene F. 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