ABSTRACT
This chapter discusses a selection of problems where dynamic localisation occurs in periodic two-dimensional lattices. It illustrates localisation for waves within a uniform one-dimensional chain of masses placed on an elastic foundation and connected by massless springs. The chapter analyses the dynamic response of both square and triangular scalar lattices with emphasis on Green's functions and the diffraction patterns generated by a point load. It is concerned with the dynamic anisotropy of discrete elastic structures in the full vector setting of planar elasticity. The chapter examines two different monatomic lattice geometries: square and triangular. It devotes to the analysis of the vector elasticity analogue of the problems presented. The chapter examines localised defect modes associated with the eigenmodes of a finite line of defects in an infinite square lattice. It devotes to the discussion of an infinite line of defects embedded in an infinite square lattice.
