Sound propagation in a solid through a screen of cylindrical scatterers

TL;DR

This paper analyzes how shear horizontal (SH) waves propagate through a solid with a uniform screen of cylindrical scatterers, providing closed-form expressions and numerical results for reflection and transmission coefficients.

Contribution

It introduces a first-order approximation with a Global Closure Assumption to evaluate coherent wave amplitudes in a scattering medium with various scatterer shapes.

Findings

Closed-form expressions for wave amplitudes inside and outside the screen.

Numerical results showing how reflection and transmission vary with frequency and scatterer concentration.

Comparison of crack and cavity scattering effects with previous studies.

Abstract

The propagation of SH waves in a solid containing a screen of line-like scatterers is investigated. When the scatterers are uniformly distributed, the amplitudes of the coherent waves inside and outside the screen are evaluated in closed form. In the analysis, multiple scattering effects are taken into account within the context of a first-order approximation. A Global Closure Assumption is proposed, which yields an effective wavenumber identical to that of Waterman and Truell. The scatterers can be fibers of circular or elliptical cross-sections; they can also be two-dimensional cracks with slit-like or elliptical cross-sections. Specific analytical and numerical results are presented for flat cracks and empty cavities of circular cross-sections. In those two cases, figures are presented to illustrate the variations of the reflection and transmission coefficients as functions of frequency and of scatterer concentration. The crack and cavity results, respectively, are compared with those of earlier works.