Band Gap Analysis of Two-Dimensional Phononic Crystals Based on Boundary Element Method

A boundary element method is developed to calculate the band gaps of out-of-plane elastic waves propagating in two-dimensional phononic crystals. The Green's function satisfying Bloch's theorem is chosen as the fundamental solution of this problem. The convergence of the sums in this Green's function is accelerated by Ewald representations. Based on the fundamental solutions, the boundary integral equations in a unit cell of the periodic structure are given, which involve integrals over the boundary between the scatterer and the matrix. Constant boundary elements are adopted to discretize the boundary. As an example, the band gaps of solid-solid binary systems are calculated and analyzed. The results show that the boundary element method is an effective numerical analysis tool.