Abstract
The problem of the vibrations of a rigid circular stamp on the surface of an elastic layer at rest on a rigid base is examined. There is no friction between the stamp and the layer, and between the layer and the base. The contact stresses under the stamp and the elastic waves originating outside the stamp are studied. A method is proposed for solving these problems at all fundamental frequencies with the exception of some singular frequencies for which another approach is necessary. The method used is based on the reduction of boundary value problems to an integral equation of the first kind, which differs from the equations investigated in static problems by strong oscillation of the kernel as well as by its bounded growth at certain frequencies. This makes known methods of investigating integral equations ineffective. The method proposed here, based on a special factorization of functions, permits overcoming the mentioned difficulties.
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