二维周期性复合介质中弹性波的能带结构

Band structure of elastic waves in the two dimensional periodic composites

用平面波展开方法，研究弹性波在二维周期性复合介质中的传播问题．由 Ｐｂ柱体嵌入 ｅｐｏｘｙ基体组成的复合介质，其弹性波带结构中，存在很大的完全带隙。研究了柱体的横截面形状、组元的体积占有率及复合介质的材料组成等因素对带结构的影响．在Ｃ柱体和ｅｐｏｘｙ基体组成的复合介质中，也观察到完全禁带的出现。但是，相反情况，由ｅｐｏｘｙ柱体和Ｐｂ或Ｃ基体组成的材料中，均无完全禁带出现。

Using the plane-waves expansion method, we study the propagation of elastic waves through the 2-D periodic composite, constructed from two different materials. We reveal the existence of several very large complete band gaps in the band structure of a material such as Pb cylinders reinforced epoxy composite. Within these gaps the propagation of elastic wave is forbidden. The influence of the geometry of the cylinders and the effect of the composition of the composite material on the band structure are studied. The complete band gaps are observed in the cases of Pb cylinders in epoxy or C cylinders in epoxy, but not in the opposite situation.