Impact response of a Timoshenko-type viscoelastic beam considering the extension of its middle surface.

In the present paper, the problem of low-velocity impact of an elastic sphere against a viscoelastic Timoshenko-type beam is studied considering the extension of its middle surface. The viscoelastic features of the beam out of the contact domain are governed by the standard linear solid model with derivatives of integer order, while within the contact domain the fractional derivative standard linear solid model is utilized, in so doing rheological constants of the material in both models are the same. However the presence of the additional parameter, i.