Dynamic stability of viscoelastic rectangular plates with concentrated masses

Abstract 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.

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