WAVE-PROPAGATION IN POLAR ELASTIC SUPERLATTICES

This paper examines the passband and stop band regions for time-period ic waves travelling normal to the layering through an infinite medium composed of alternating layers of two different elastic materials. The materials are such that the elastic energy density is a function of t he strains and the strain gradients and, in consequence, a deformation gives rise to both the usual Cauchy stress and to a hyperstress or co uple-stress. Such materials can exhibit a non-uniform wrinkling deform ation at a free surface and similar non-uniform deformations can arise at interfaces between two different media. The presence of the strain derivatives in the elastic energy function introduces a natural lengt h scale l into the material and the depth of the non-uniform deformati on is of the order of this length scale. This model can give rise to e nhanced elastic response when the layer depths are comparable with l a nd it is of interest as a possible mathematical model of nanolayered s tructures. The model also includes a non-standard set of continuity co nditions at material interfaces. These arise from the elastic interact ion energy of the two materials at the boundary and their effect is lo calized in a boundary layer whose depth is of order 1. The periodic la yering gives rise to displacements which are periodic with a frequency -dependent wave number, the Floquet wave number. Dispersion curves, re lating circular frequency to the Floquet wave number, are obtained for different ratios of the layer depth to the natural length l and for d ifferent values of the elastic interface coupling parameters.