Parametric oscillations of viscoelastic orthotropic plates of variable thickness

Viscoelastic orthotropic rectangular plates of variable thickness are considered in the paper under the effect of periodic load. It is believed that under periodic load, the plates allow displacements commensurate with their thickness. Based on the Kirchhoff-Love hypothesis, a mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic rectangular plate of variable thickness is constructed in a geometrically nonlinear statement. A method for solving the problem under consideration is proposed, based on the application of the Bubnov-Galerkin method with polynomial approximation of displacements and deflection, and on a numerical method based on the use of quadrature formulas. In calculations, the three-parameter Koltunov-Rzhanitsyn kernel is used as a weakly singular kernel. Based on the algorithm for solving the problem, a program was developed in the Delphi algorithmic language to solve the problem of parametric oscillations of viscoelastic orthotropic rectangular plates of variable thickness under the effect of an external periodic load. The effect of geometrical nonlinearity, viscoelastic properties of the material, physico-mechanical and geometrical parameters of a viscoelastic orthotropic plate on the areas of dynamic instability was investigated. The results obtained are in good agreement with the results of other authors.