Abstract
Boundary element method (BEM) is employed to compute the transmission of two-dimensional (2D) three-phase phononic crystals. The system is in a square lattice which has finite layers along the x-direction and is infinite along y-direction. The cross sections of the inclusions are circular. In a periodic unit cell, boundary integral equations of the matrix, the coating and the inclusion are given. A linear equation set is formed by substituting the periodic boundary conditions and the interface conditions, from which the transmission response can be obtained. Then the band gaps of the phononic system can be found. The obtained results are basically consistent with the band structures from the corresponding infinite systems. It is shown that the present method can accurately compute the transmission.
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