Contact problems of the sliding of a punch with a periodic relief on a viscoelastic half-plane

A method is proposed for the analytical solution of problems of the sliding of a punch with a periodic relief on a viscoelastic half-plane under conditions when they are in complete contact as well as problems on the loading of a viscoelastic half-plane with a piecewise-constant pressure that moves at a constant velocity on its surface. The problems are considered in a quasistatic formulation. The method is based on the expansion of the sought functions in trigonometric Fourier series and finding the relation between the displacements of the boundary and the contact pressures. Examples of different shapes of punches are considered and the dependencies of the contact characteristics and the mechaical component of the friction force on the sliding velocity, the viscosity parameters of the base and the geometric characteristics of the surface are studied.