Locally resonant phononic crystals band-gap analysis on a two dimensional phononic crystal with a square and a triangular lattice

Locally resonant phononic crystals (LRPC) are a new type of sound insulating material. Using the plane wave expansion method based on the Bloch theorem, we compute the band structure of two dimensional (2D) phononic crystals (PC) with square and triangular lattices. Such PC typically consists of infinitely long carbon rods coated with silicon rubber and embedded in an elastic background. Computational results show that gaps appear at the lower frequency range, which are lower than those expected from the Bragg mechanism. Those gaps are generated due to local resonances; the optimum gap is obtained by tuning the thickness ratio of the coating layer. The gap created by the LRPC depends on the filling fraction of the coating cylinders.