Elastic waves and homogenization in oblique periodic structures
Elastic waves and homogenization in oblique periodic structures
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斜周期结构中的弹性波和均匀化
DOI：
10.1098/rspa.2001.0948
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
R. McPhedran
中科院分区：
文献类型：
--
作者：
V. Zalipaev;A. Movchan;C. Poulton;R. McPhedran
建立了描述弹性波在含有双周期平行四边形圆孔阵列的二维固体中传播的数学模型。采用多极展开法，通过牵引力边界条件考虑了剪切波和伸缩波的耦合，确定了传播模式的结构。重要的是，均匀的弹性结构是各向异性的；这是从这里给出的分析得出的。该算法已被实现到计算机程序中，用它来构造弥散图并分析复合材料结构的滤波特性。研究具有声子带隙的平行四边形晶格的六边形和菱形型格子是特别有意义的。
A mathematical model has been constructed to describe elastic waves propagating in a two–dimensional solid containing a doubly periodic parallelogram array of circular holes. A multipole expansion method is employed which takes into account a coupling between shear and dilatational waves via the traction boundary conditions and determines the structure of the propagating modes. It is important that the homogenized elastic structure be anisotropic; this follows from analysis presented here. The algorithm has been implemented into a computer code, which was used to construct the dispersion diagrams and analyse the filtering properties of the composite structure. It is of particular interest to study the hexagonal and rhombic types of parallelogram lattices, which can be shown to exhibit phononic band–gaps.