中文摘要：

发展了计算二维三组元局域共振型声子晶体带隙结构的边界元法,该方法在一个单胞内分别对基体和含有包覆层的嵌入体（三相材料）建立边界积分方程,在基体边界上施加Bloch条件,并考虑不同相之间的界面条件后得到一个线性的特征值方程。该方法的计算结果和对应的二组元体系计算结果进行了比较,结果表明,在三相体系中声波发生局部共振,此时中间包覆层材料的作用类似于一个软弹簧;而且由于包覆层材料的密度很低且声速很小,所以对应的系统共振频率较低,使声带隙出现在较低频段。另外,本文还分析了＂包覆层＂材料的特性以及边界元法计算三组元声子晶体的特点。

英文摘要：

The band structures of the two-dimensional three-component locally resonance phononic crystal were calculated by boundary element method. In a unit cell,the boundary integral equations of the matrix and the coated scatterers（ three-phase materials） were derived. By substituting the Bloch periodic boundary conditions and the interface conditions between different phases,a linear eigenvalue equation was derived. The obtained results were compared with those of the corresponding two-phase systems. The results show that the local resonance occurs in three-phase systems,and that the middle coated material acts as a soft spring; because of its low density and small acoustic velocity,the corresponding resonance frequency is low,which makes the band gap appear in the low frequency. Additionally,the properties of the coated material and the boundary element method were analyzed.