Band gaps calculation of scalar waves in two-dimensional phononic crystals with Generalized Multipole Technique (GMT)

A numerical method based on the Generalized Multipole Technique (GMT) is proposed to calculate the band gaps of scalar waves in two-dimensional phononic crystal, which is composed of arbitrary shape cylinders embedded in a host medium in square lattice. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalue can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone (FBZ), the band structure will be obtained. Some numerical examples are illustrated to validate the present method.