Analysis of Vibrations of an Elastic Plate On a Viscoelastic Base Via the Fractional Derivative Kelvin-voigt Model

In the present paper, free and forced vibrations of an elastic Kirchhoff-Love plate on a viscoelastic foundation of the Fuss-Winkler type are studied, the damping properties of which are described using the Kelvin-Voigt model with a fractional derivative. The integral Laplace transform method with further expansion of the sought functions into a series of eigenfunctions of the problem is used as the method for solving the problem of non-stationary vibrations of linear elastic plates on a viscoelastic foundation. The solution is obtained as the sum of two terms, one of which controls the drift of the equilibrium position of the system and is determined by the quasi-static creep processes occurring in the system, and the other term describes the damping of oscillations around the equilibrium position and is determined by the inertia and energy dissipation of the system.