On Antiplane Waves Localized in the Vicinity of the Interface of Two Elastic Half-Spaces in the Framework of Lattice Dynamics

We consider antiplane waves that are localised in the vicinity of the interface between two elastic half-spaces. The problem is formulated within the context of the dynamics of a square lattice. Accordingly, the interface region comprises particles with a different mass to the particles in the bulk and with different elastic bonds. For this model, we demonstrate the possibility of two types of wave being localised in the vicinity of the interface. The corresponding dispersion relations are obtained. The results are compared with the Gurtin-Murdoch theory of surface elasticity.