Reflection and transmission by randomly spaced elastic cylinders in a fluid slab-like region

Abstract

An extension of Fikioris and Waterman’s formalism is developed in order to describe both the reflection and transmission from a slab-like fluid region in which elastic cylindrical scatterers are randomly placed. The dispersion equation of the coherent wave inside the slab must be solved numerically. For solid cylinders, there is only one solution corresponding to a mean free path of the coherent wave larger than one wavelength. In that case, the slab region may be described as an effective dissipative fluid medium, and its reflection and transmission coefficients may be formally written as those of a fluid plate. For thin hollow shells, a second solution of the dispersion equation is found, at concentrations large enough for the shells to be coupled via the radiation of a circumferential Scholte–Stoneley A wave on each shell. This occurs at a few resonance frequencies of the shells. At those frequencies, then, two different coherent waves propagate in the slab, and it can no longer be considered a dissipating fluid slab.