Interaction of Elastic Dilatational and Shear Waves With a Frictional Sliding Interface

Abstract

The refraction and reflection of plane dilatational and shear waves, which are incident upon a sliding frictional interface between two elastic half-spaces, is considered. The contact interface is governed by Coulomb’s friction law with a constant friction coefficient. The incoming waves interact with the interface to form two reflected waves (shear and dilatational) as well as two such refracted waves. The dependency of the reflected and refracted wave amplitudes on the incoming wave angle is investigated. It is shown that the contact normal stress, shear stress and relative sliding velocity are proportional to each other. The interaction of an isolated interfacial rectangular wave pulse, or of a periodic set of pulses, with the frictional interface is then investigated. It is shown that steady motion of the two bodies can result due to the propagation of interface stick-slip waves. This motion can occur in the same direction or in the opposite direction of the remotely applied shear traction, or without an applied shear traction. The velocity of relative motion as a function of material parameters, friction coefficient, remotely applied shear and normal tractions, and parameters of the pulse is presented and discussed. These results may lead to a new form of ultrasonic propulsion which can be utilized for position or velocity control of a sliding body.