Архив выпусков

The construction of analytic solution of a problem of stick-slip waves crossing the interface between an elastic half-space and a rigid one under unilateral contact and Coulomb's friction is considered. The method of solution is based on the analytic continuation method of Radok's complex potentials within the framework of steady elastodynamical problems. The governing equations combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient and closed-form expressions of the solution are derived. It is found that the existence of solutions depends on the additional velocity which is related to the longitudinal elongation. If this velocity is ignored, then there is no solution, if not, then it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone where the waves exhibit a crack-like behaviour.