Surface Waves Guided by a Slit in an Elastic Solid

Wave propagation in an isotropic elastic solid containing a slit is studied. The slit is viewed as an open crack of finite width and infinite length. In particular, the propagation of surface waves on the faces of the slit is considered. Making use of a reflection law for the oblique reflection of a Rayleigh wave from the tip of an open half-plane crack, surface waves are superimposed to form guided surface waves in the slit. In order to carry out the construction of dispersion relations, an assumption on the rate of decay of body wave modes localized in the vicinity of the edges of the guide is made, and the range of validity of the assumption is discussed. The dispersion relations are obtained by geometrical construction, and representative dispersion curves are shown.