Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical Cavity

Abstract

Oscillations of a viscoelastic medium with a cylindrical cavity are studied. The viscosity is taken into account in the form of an additional term in the constitutive equation, proportional to a fractional derivative of variable order. In the considered examples the order function corresponds to dependences obtained for real materials. A damping effect is observed in the amplitude behavior. The field which determines the order function demonstrates the viscoelastic behavior of the material under load.