Impact of a body against a rigid wall. Problem involving non-smooth and history dependent energy dissipation mechanism

We study the impact of a body against a rigid wall. The body consists of a rigid block and a viscoelastic rod described by the fractional Zener model. Translatory motion of a body is influenced by the dry friction, described by the set-valued Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form. These solutions are compared with the ones obtained by using the numerical method.