Transmission and reflection at the boundary of a random two-component composite
Transmission and reflection at the boundary of a random two-component composite
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随机双组分复合材料边界处的透射和反射
DOI：
10.1098/rspa.2019.0811
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
J. Willis
中科院分区：
文献类型：
--
作者：
J. Willis
半空间x2 >； 0被具有指定体积分数和两点关联的两分量统计均匀随机复合材料占据。它被束缚在均匀的半空间x2 <； 0上，平面波从该半空间入射。通过最佳利用给定统计信息的变分公式来计算透射和反射的平均波。这个问题需要说明三种介质的性质：复合材料的两种成分的性质和均匀半空间的性质。通过考虑三种介质具有相同的模数但不同的密度的模型声波问题，使问题的复杂性最小化。它被描述为Wiener-Hopf型问题，在相关函数呈指数衰减的特殊情况下被显式求解。在简短的结束语部分讨论了可能的概括。
A half-space x2 > 0 is occupied by a two-component statistically uniform random composite with specified volume fractions and two-point correlation. It is bonded to a uniform half-space x2 < 0 from which a plane wave is incident. The transmitted and reflected mean waves are calculated via a variational formulation that makes optimal use of the given statistical information. The problem requires the specification of the properties of three media: those of the two constituents of the composite and those of the homogeneous half-space. The complexity of the problem is minimized by considering a model acoustic-wave problem in which the three media have the same modulus but different densities. It is formulated as a problem of Wiener–Hopf type which is solved explicitly in the particular case of an exponentially decaying correlation function. Possible generalizations are discussed in a brief concluding section.