Open AccessDynamic stability of viscoelastic rectangular plates with concentrated masses
Author(s) -
Dadakhan Khodzhaev,
Rustamkhan Abdikarimov,
Bakhodir Normuminov
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/896/1/012030
Subject(s) - viscoelasticity , galerkin method , orthotropic material , nonlinear system , nyström method , boundary value problem , stability (learning theory) , dirac delta function , quadrature (astronomy) , mathematical analysis , equations of motion , mathematics , polynomial , classical mechanics , materials science , physics , structural engineering , computer science , engineering , composite material , finite element method , optics , quantum mechanics , machine learning
Thin-walled constructions such as plates and shells, with installed units, devices and assemblies, are widely used in engineering and construction. In calculations, such attached elements are considered as concentrated at points and rigidly fixed elements. The influence of concentrated masses is taken into account in the equation of motion using the Dirac delta function. Recently, more and more attention has been paid to the nonlinear and inhomogeneous properties of a structure. Dynamic stability of viscoelastic orthotropic rectangular plates with concentrated masses in a geometrically nonlinear statement is considered in the paper. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations. The results of the problem are obtained by the proposed numerical method based on the use of quadrature formulas. Dynamic stability of viscoelastic rectangular plates with concentrated masses under various boundary conditions was studied over a wide range of changes in physico-mechanical and geometrical parameters of the plate.