A boundary element method (BEM) is implemented and applied to compute the band structures of phononic crystals taking account of three different kinds of imperfect interface layers. By using the Bloch theorem and the interface conditions the eigenvalue equations related to the wave vector are derived. The influences of the spring-interface model, mass-interface model and spring-mass-interface model on the dispersion curves and the band-gaps are investigated by comparing with that of the perfect interfaces. For different interface models, the effects of various interface parameters and mass density ratios on the lower edge, upper edge and width of the first complete band-gap are analyzed and discussed. It will be shown that a weak interface imperfection would not affect the dispersion curves, but a relatively strong interface imperfection may significantly affect the band structures of phononic crystals and it cannot be ignored. Moreover, the three interface models have different influences on the wave propagation and band-gap characteristics of the phononic crystals.

考虑到三种不同类型的不完美界面层，实现并应用边界元法 (BEM) 来计算声子晶体的能带结构。通过使用布洛赫定理和界面条件，推导出与波矢相关的特征值方程。通过与完美界面的比较，研究了弹簧界面模型、质量界面模型和弹簧质量界面模型对色散曲线和带隙的影响。针对不同的界面模型，分析讨论了各种界面参数和质量密度比对第一完全带隙的下边缘、上边缘和宽度的影响。将表明弱界面缺陷不会影响色散曲线，但相对较强的界面缺陷可能会显着影响声子晶体的能带结构，不容忽视。此外，三种界面模型对声子晶体的波传播和带隙特性有不同的影响。