Laboratorium voor Akoestiek en Thermische Fysica, KULeuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
J Acoust Soc Am. 2011 Sep;130(3):1390-8. doi: 10.1121/1.3605530.
Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives.
近年来，宏观非均匀多孔材料中的波传播受到了广泛关注。最近，根据比奥 1962 年理论的替代公式，在刚性框架非均匀多孔材料的情况下，对波动方程进行了简化和求解。本文重点研究了全波方程的解，其中多孔弹性材料的声学和弹性特性在一维空间中发生变化。使用状态向量（或所谓的 Stroh）形式和 Peano 级数，通过数值方法获得了一维宏观非均匀多孔材料在刚性背衬上的反射系数。然后，该系数可直接用于计算散射场。为了验证解析方法，将通过本方法获得的结果与经典传递矩阵方法在法向和斜入射以及在已知的两层多孔材料（视为单层非均匀层）的法向入射的实验测量结果进行了比较。最后，对各种非均匀性分布的吸收系数进行了讨论，为进一步的研究提供了思路。
