Dynamic Stability of Viscoelastic Orthotropic Rectangular Plate with Variable Thickness Under Periodic Loads

A mathematical model of the problem of parametric vibrations of viscoelastic rectangular orthotropic plates of variable thickness under periodic load is given in the paper. It is believed that under the effect of this load, the plates undergo the displacements commensurate with their thickness. Geometrically nonlinear mathematical model of the problem of parametric vibrations of a viscoelastic plate of variable thickness is developed using the Kirchhoff-Love hypothesis. The mathematical model of this problem is constructed taking into account the propagation of elastic waves. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflection and displacements, the problem is reduced to solving systems of nonlinear integro-differential equations with variable coefficients. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric vibrations of viscoelastic plates of variable thickness under the effect of an external load are investigated. The effects of viscoelastic properties of the material and changes in thickness on the oscillation process are studied.