Anti-plane surface waves localized in multi-layered interfaces in square-lattice structures

We investigate the propagation of anti-plane shear waves localized within a multi-layered interface of a square lattice. The structure consists of two infinite half-spaces, either identical or dissimilar in their bulk properties, separated by a three-row interface that may be stiffer or softer than the surrounding media. A discrete square-lattice model is employed, in which particles of mass are connected by elastic bonds whose properties vary between regions. Using a lattice-dynamics approach, we derive the dispersion relation for waves propagating along the interface for different material contrasts between the bulks and the interface.