Open AccessFree vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis
Author(s) -
V.C. Haciyev,
Гаджиев Вагиф Джамал Оглы,
Gulnar R. Mirzoeva,
Мирзоева Гюлнар Ровшан Кызы,
Matlab G. Agayarov,
Агаяров Матлаб Гусейнгулу Оглы
Publication year - 2019
Publication title -
stroitelʹnaâ mehanika inženernyh konstrukcij i sooruženij
Language(s) - English
Resource type - Journals
eISSN - 2587-8700
pISSN - 1815-5235
DOI - 10.22363/1815-5235-2019-15-6-470-476
Subject(s) - orthotropic material , viscoelasticity , vibration , galerkin method , boundary value problem , plate theory , anisotropy , materials science , classical mechanics , mechanics , mathematical analysis , physics , mathematics , nonlinear system , acoustics , optics , composite material , finite element method , quantum mechanics , thermodynamics
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.