Axisymmetric Problem of Vibrations of Circular or Ring Punch on Elastic Half-Space*

The axisymmetric contact problem on steady vibrations of a circular or ring punch on an elastic half-space without taking into account friction forces is considered. Convenient and efficient formulas for the displacements of the elastic foundation are obtained. These formulas were used in the formulation of integral equations for the unknown contact stress, which allowed to apply the method of orthogonal polynomials to the solution. The dependence of the contact stress amplitudes on the mass and vibration frequency of the punch is studied.