On the Oscillation of a Punch Moving on Free Surface of an Elastic Half-Space

The contact problem concerning oscillation of a circular rigid punch moving uniformly at a sub-rayleigh speed along the surface of an elastic half-space is investigated in three-dimensional statement. “Slow” motion of the punch is considered: it is supposed that characteristic time for external loading is much greater than time interval of shear wave propagation along the punch. It is shown that in first approximation the vertical displacement of the punch can be described by equation of dynamics for one degree of freedom system with viscous friction. Coefficients of effective viscosity and stiffness of the elastic half-space are found as functions of speed of the punch and Poisson ratio. The solution for non-stationary problem concerning suddenly applied moving point constant surface load is obtained, which corrects the known result.