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We present a comparison of the dispersion relations derived for anti-planesurface waves using the two distinct approaches of the surface elasticityvis-a-vis the lattice dynamics. We consider an elastic half-space with surfacestresses described within the Gurtin-Murdoch model, and present a formulationof its discrete counterpart that is a square lattice half-plane with surfacerow of particles having mass and elastic bonds different from the ones in thebulk. As both models possess anti-plane surface waves we discuss similaritiesbetween the continuum and discrete viewpoint. In particular, in the context ofthe behaviour of phase velocity, we discuss the possible characterization ofthe surface shear modulus through the parameters involved in latticeformulation.

Anti-plane surface waves in media with surface structure: discrete vs. continuum model