Abstract
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 on the basis of the Kirchhoff–Love hypothesis in a geometrically nonlinear statement. 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 effects of viscoelastic properties of the material and changes in thickness on the oscillation process are studied.
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