Summary of the

This paper examines the passband and stop band regions for time-periodic 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 the strains and the strain gradients and, in consequence, a deformation gives rise to both the usual Cauchy stress and to a hyperstress or couple-stress. Such materials can exhibit a non-uniform wrinkling deformation 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 length scale 1 into the material and the depth of the non-uniform deformation is of the order of this length scale. This model can give rise to enhanced elastic response when the layer depths are comparable with 1 and it is of interest as a possible mathematical model of nanolayered structures. The model also includes a non-standard set of continuity conditions at material interfaces. These arise from the elastic interaction energy of the two materials at the boundary and their effect is localized in a boundary layer whose depth is of order 1. The periodic layering gives rise to displacements which are periodic with a frequency-dependent wave number, the Floquet wave number. Dispersion curves, relating circular frequency to the Floquet wave number, are obtained for different ratios of the layer depth to the natural length 1 and for different values of the elastic interface coupling parameters