2023/09/15 by Sharma, Basant Lal
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2309.08552
In current scientific and technological scenario, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analog of Gurtin-Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work of Sharma & Eremeyev 2019 Int. J. Eng. Sci. 143, 33-38 is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.