Surface/interface effects on dispersion relations of 2D phononic crystals with parallel nanoholes or nanofibers

Owing to the increasing ratio of surface to bulk volume, surface effects emerge in the mechanical performance of devices and materials when the characteristic size reduces to nanoscale. In this paper, the dispersion relations and the band gap properties of 2D phononic crystals with periodically arranged nanoholes or nanofibers are studied. The scattering matrix of a single scatterer is first derived from a set of nontraditional boundary conditions based on the surface elasticity theory. Then, the addition theorem of cylindrical waves and Bloch’s theorem of periodical structure are used to obtain the dispersion relations of an elastic wave polarized in the plane perpendicular to the axis of the nanoholes or nanofibers. It is found that the surface effect has remarkable influences on the dispersion relations and the band gaps for the phononic crystal with nanoholes. For the 2D phononic crystal with periodical arranged nanofibers, the interface effect is more evident for the softer fibers than for the stiffer fibers.