含随机圆柱散射体弹性介质的有效波数和反射系数
Effective wavenumbers and reflection coefficients for an elastic medium containing random configurations of cylindrical scatterers
摘要：
研究了P波和SV波在半空间中含有随机分布夹杂的弹性固体中的传播。该方法是基于一个类似的Fikioris和Waterman提出的标量波的多次散射分析。特征方程，其中的解决方案产生的相干弹性波的有效波数，得到在一个明确的形式，而不使用任何重整化方法。两个近似被认为是。首先，公式推导出在稀疏随机分布的相同的散射体的有效波数。这些方程推广了Linton和Martin关于标量相干波的公式。其次，高频近似与沃特曼和Truell的方法在这里推导出的弹性波进行了比较。与Waterman和Truell的方法相比，Fikioris和Waterman的方法表明，即使在散射体浓度相对较低的情况下，P波和SV波也是耦合的。本文还导出了P波和SV波入射到含随机夹杂半空间界面上反射系数的简单表达式。这些表达式依赖于频率，散射体的浓度，以及在弹性多次散射介质中传播的相干波的两个有效波数。
英文摘要：
Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for scalar waves. The characteristic equation, the solution of which yields the effective wave numbers of coherent elastic waves, is obtained in an explicit form without the use of any renormalisation methods. Two approximations are considered. First, formulae are derived for the effective wave numbers in a dilute random distribution of identical scatterers. These equations generalize the formula obtained by Linton and Martin for scalar coherent waves. Second, the high frequency approximation is compared with the Waterman and Truell approach derived here for elastic waves. The Fikioris and Waterman approach, in contrast with Waterman and Truell's method, shows that P and SV waves are coupled even at relatively low concentration of scatterers. Simple expressions for the reflected coefficients of P and SV waves incident on the interface of the half space containing randomly distributed inclusions are also derived. These expressions depend on frequency, concentration of scatterers, and the two effective wave numbers of the coherent waves propagating in the elastic multiple scattering medium.
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