Two-Dimensional Waves in A Chiral Elastic Chain: Dynamic Green's Matrices and Localised Defect Modes

This article presents new analytical work on the analysis of waves in chiral elastic chains. The notion of dynamic chirality, well established and explored for electromagnetic waves in magnetised media, is less common for elastic solids. Indeed, it is even less common to observe vector wave problems in an elastic chain. Here, it is shown that the physical system, described by a vector formulation for waves in a chiral chain, can simultaneously support Floquet–Bloch waves in addition to localised waveforms, subject to the appropriate choice of the frequency interval. We construct and analyse dynamic Green’s matrices and identify exponentially localised defect modes, which correspond to spatially confined elliptical motion of nodal inertial elements, around the perturbed cell of the chiral chain. Special attention is given to the case of the dynamic degeneracy. Analytical findings are accompanied by numerical illustrations and examples.