Acoustic band gaps in fibre composite materials of boron nitride structure

We present elastic band-structure results for a new geometry of two-dimensional phononic crystals: the boron nitride- (BN-) like structure. This array is constituted of two kinds of infinite elastic parallel cylinder located at the vertices of a regular hexagon and surrounded by an elastic background. This geometry includes both the triangular and graphite structures as particular cases. The inclusions and matrix are either both fluids or both solids, the constituent materials being water and mercury, and carbon (or tungsten) and epoxy. We discuss the evolution of the band structure, and especially the existence of absolute band gaps, as a function of the ratio between the radii of the two cylinders in the BN geometry. We also discuss the existence of these gaps in relation to the physical parameters of the materials involved, and compare the results with those for square and triangular structures.