Radiation of body waves induced by the sliding of an elastic half-space against a rigid surface

The steady sliding of a flat half-space against a rigid surface with a constant interfacial coefficient of friction is investigated. it is shown here that steady sliding is compatible with the formation of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different tingle such that the trace velocities along the interface are equal and supersonic with respect to the elastic medium. The angles of wave propagation are determined by the Poisson's ratio and by the coefficient of friction, The amplitude of the waves are indeterminant, subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that a rectangular wave train or a rectangular pulse, can allow for motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. Furthermore it is shown that the apparent friction coefficient decreases with increasing speed even if the interface friction coefficient is speed-independent. This result supports the interpretation of certain friction behavior as being a consequence of the dynamics of the system, rather than strictly as an interface property. In fact no distinction is made between the static and kinetic interface fiction coefficients.