Bandgap analysis of two-dimensional phononic crystals

The Dirichlet-to-Neumann method is adopted to calculate the band gaps of the two-dimensional phononic crystals with different interface conditions.The system is in a square lattice which is composed of the solid cylinders embedded in a softer material.The cross sections of the inclusions are circular.In a unit cell a linear eigenvalue equation is formulated, from which the band gaps can be obtained.A typicla numerical example is taken to analyze and discuss the roles of the interface conditions.The results show that the Dirichlet-to-Neumann method can provide accurate results and the different interface conditions have significant effects on the band gaps.