LINE WAVES IN ELASTIC METAMATERIALS

Line modes have been recently identified in electromagnetic materials: one dimensional waves bound to surfaces with opposite sign of permittivity and permeability. Here, we communicate analogous elastic line waves in mechanical metamaterials, using both analytical theory and the finite element method. We show analytically that a pure shear line mode exists at the boundary of an elastic material, at a junction between a region where the boundary is pinned in the plane, and out of the plane. We also numerically investigate the properties of line waves for the inverse situation where the boundary condition of the elastic media is fixed, but the sign of bulk material properties abruptly change. The eigenfrequency of line modes at an interface between bulk metamaterials can be tuned by varying the mass density of the materials.