Slow vertical motions of a system of punches on an elastic half-space

The slow dynamic contact interaction between several arbitrary smooth punches with a homogeneous isotropic elastic half-space is considered. An asymptotic solution of the problem is constructed under the assumption that the contact pressures under the punches are slightly varied during the time of travel of the Rayleigh wave along the distance compared with the diameters of the contact areas. The first order asymptotic model suitable for a large number of punches is constructed. The second order asymptotic model is written out in the case of a system of circular punches.