Abstract
A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.
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Li, F., Wang, Y. & Zhang, C. Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals. Sci. China Phys. Mech. Astron. 59, 664602 (2016). https://doi.org/10.1007/s11433-015-0501-x
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DOI: https://doi.org/10.1007/s11433-015-0501-x