Large two-dimensional sonic band gaps

Abstract

In this paper it is shown that a two-dimensional honeycomb structure is a good candidate to produce large full band gaps in sonic band gap (SBG) materials. The full gap of the honeycomb lattice can be increased by reducing the symmetry of the cell as it occurs in photonic band gap (PBG) materials. The evolution of the band gap in the honeycomb-triangular transition has been studied. Starting from a honeycomb lattice (with 4 cm diameter cylinders), one can study the transition to a triangular symmetry by placing rods with different diameter (from 0.6 to 4 cm) at the center of the honeycomb lattice. When the diameter cylinder of the center of the unit cell has the same diameter as cylinders of the unit cell (4 cm), the lattice achieves a triangular symmetry. The obtained results are compared with theoretical calculations performed with a variational method.