Frictional contact between the surface wave and a rigid strip

A problem of frictional contact between a running surface wave and a motionless rigid strip is considered. The corresponding mixed boundary value problem of elastodynamics is reduced to a singular integral equation for the normal stress distribution and a closed-form solution of it has been found. Boundaries of the contact zone are determined from a system of transcendental equations involving trigonometric functions. Also, simple formulae obtained for kinematic characteristics of solution (tangential velocity inside the contact area, velocity and slope of the free surface outside it). The problem considered represents a limiting case of operating ultrasonic motor when it is completely braked by an external tangential load force.