The two-dimensional phononic crystal band gaps tuned by the symmetry and orientation of the additional rods in the center of unit cell

Abstract

The effects of symmetry and orientation of the additional steel rods on the band gaps of two-dimensional phononic crystals with steel-air system are numerically investigated by using the plane wave expansion method. The original steel rods of the phononic crystals are of columns in square and hexagonal lattices, and the additional steel rods are of regular square, hexagon, octagon prisms and columns, which are placed, respectively, in the center of each unit cell of the two kinds of lattices. The gap maps are introduced to illustrate the influences of the filling fraction and orientation of the additional rods on band gaps. It is found that in the case of the additional rods with low filling fraction, the band gaps can be obtained most easily because the degeneracy of bands is lifted when the cross section of additional rod has the same shape as that of lattice, but the widest band gaps appear under the condition of the additional rods with highest symmetry and largest filling fraction. The influence of orientation on band gap in square lattice is more obvious than that in hexagonal lattice. If the column lattice points are changed by square prisms in simple square lattice, the lower and wider band gaps can be produced by rotating the square prisms, which is contrary to the scenario that emerges in square lattice with additional rods at the center of unit cell. Using one of the methods of adding additional rods or rotating the original prisms is more beneficial to the generation of band gaps than combining effect of these two means in simple lattices. Furthermore, the mechanisms of above results are analyzed.