中文摘要：

基于超胞技术,边界元法被推广到计算二维正方晶格声子晶体的缺陷态。该方法是在一个超胞内分别对基体和各个散射体建立边界积分方程,在基体边界上施加Bloch条件,并考虑基体和散射体之间的界面条件后得到一个线性的特征值方程。为了验证该方法的正确性,分别对固/流体系和固/固体系的点缺陷和线缺陷进行了计算和分析,并与其他方法的计算结果进行了比较,结果表明：边界元法计算含缺陷的声子晶体是可行和有效的,同时缺陷态的特性为声学器件的设计提供了思路。

英文摘要：

Based on the supercell technique,a boundary element method（ BEM） is extended to calculate the defect states of the two-dimensional phononic crystals in a square lattice. In a supercell,the boundary integral equations of the matrix and the scatterers are derived. By substituting the Bloch periodic boundary conditions and the interface conditions between the matrix and the scatterers,a linear eigenvalue equation is derived. To check the accuracy of the boundary element method,the point and line defects of the solid / fluid and solid / solid systems are calculated and analyzed,and the obtained results are compared with those computed by other methods. It is shown that the boundary element method is feasible and effective for the calculation of the phononic crystals with defects,and the properties of the defect states provide a new way to design the acoustic devices.