Wave transmission across surface interfaces in lattice structures

TL;DR

This paper provides an exact solution for anti-plane surface wave transmission in a lattice structure with an interface of different surface elastic properties, highlighting the effects of surface inhomogeneity on wave behavior.

Contribution

It introduces a discrete lattice model for surface wave transmission across an elastic interface, extending continuum models to lattice dynamics with exact solutions.

Findings

Surface inhomogeneity affects wave transmittance and reflectance.

Exact solutions reveal influence of grain boundaries on surface waves.

Surface elastic property differences alter wave propagation characteristics.

Abstract

Within the lattice dynamics formulation, we present an exact solution for anti-plane surface waves in a square lattice strip with a surface row of material particles of two types separated by a linear interface. The considered problem is a discrete analog of an elastic half-space with surface stresses modelled through the simplified Gurtin-Murdoch model, where we have an interfacial line separating areas with different surface elastic properties. The main attention is paid to the transmittance and the reflectance of a wave across the interface. The presented results shed a light on the influence on surface waves of surface inhomogeneity in surface elastic properties such as grain and subgrain boundaries.