Slow vertical motions of a punch on an elastic half-space

An asymptotic solution to the problem of a punch of an arbitrary fixed lateral shape under the assumption that the contact pressure under the punch base is varied during the time of travel of the Rayleigh wave, was constructed. The construction of the terms of the asymptotic expansion for the contact pressure is reduced to the solution of the integral equation for a quasistatic contact problem. In the case of steady state oscillation, the expansions correspond to expansions for a circular punch at low frequencies. The fixed value of the diameter of the punch base and the assumption about slowness of the punch motion,means that the relative frequency of oscillations is low.