Modeling of the Impact Response of a Beam in a Viscoelastic Medium

In the present paper, we consider the problem on a transverse impact of a viscoelastic sphere upon an elastic Bernoulli-Euler beam in a viscoelastic medium, the viscoelastic features of which are described by certain viscoelastic operators. The Young's modulus of the impactor is the time-dependent operator, which is defined via the standard linear solid fractional derivative model, while the bulk modulus is considered to be constant. Within the contact domain the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving in the problem under consideration, the algebra of Rabotnov's fractional operators is employed. The integral equation is obtained for the contact force.