基于斜向SH波散射的对称层状介质整体本构描述
Overall constitutive description of symmetric layered media based on scattering of oblique SH waves
摘要：
本文研究了由弹性层和粘弹性层组成的有限周期介质对斜向剪切水平波的散射。它进一步考虑是否威利斯型本构矩阵（在时间和空间傅立叶域）可以重现这样的系统的散射矩阵（SM）。在回答这个问题的程序来确定相关的整体本构参数，这样的介质。为了做到这一点，第一的一般形式的色散关系和阻抗的斜SH传播在这样的耦合威利斯型介质的开发。采用传输矩阵法计算了层状介质的能带结构和散射特性。色散关系可以基于无限周期域的本征解导出。与有限厚度平板的外表面相关联的波阻抗从这样的系统的散射中提取。基于结构和每个组成层的互易性和可用对称性，可以简化色散和阻抗的一般形式。通过将TM的散射数据与Willis型介质的预期散射数据相等，可以提取总数量。很明显，一个威利斯型耦合本构张量的组件，假设独立的波矢量是无法重现所有的斜散射数据。因此，非唯一的波矢量相关的配方，其SM匹配的层状介质完全。它进一步表明，这种系统的整体本构张量的波矢量的依赖性是不可移除的，即使在非常小的频率和入射角和分析的考虑显着限制的潜在形式的空间色散本构张量。
英文摘要：
This papers investigates the scattering of oblique shear horizontal (SH) waves off finite periodic media made of elastic and viscoelastic layers. It further considers whether a Willis-type constitutive matrix (in temporal and spatial Fourier domain) may reproduce the scattering matrix (SM) of such a system. In answering this question the procedure to determine the relevant overall constitutive parameters for such a medium is presented. To do this, first the general form of the dispersion relation and impedances for oblique SH propagation in such coupled Willis-type media are developed. The band structure and scattering of layered media are calculated using the transfer matrix (TM) method. The dispersion relation may be derived based on the eigensolutions of an infinite periodic domain. The wave impedances associated with the exterior surfaces of a finite thickness slab are extracted from the scattering of such a system. Based on reciprocity and available symmetries of the structure and each constituent layer, the general form of the dispersion and impedances may be simplified. The overall quantities may be extracted by equating the scattering data from TM with those expected from a Willis-type medium. It becomes evident that a Willis-type coupled constitutive tensor with components that are assumed independent of wave vector is unable to reproduce all oblique scattering data. Therefore, non-unique wave vector dependent formulations are introduced, whose SM matches that of the layered media exactly. It is further shown that the dependence of the overall constitutive tensors of such systems on the wave vector is not removable even at very small frequencies and incidence angles and that analytical considerations significantly limit the potential forms of the spatially dispersive constitutive tensors.
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