Effective conditions for the reflection of an acoustic wave by low-porosity perforated plates

International audienceThis paper describes an investigation of the acoustic properties of a low-porosity perforated plate in a compressible ideal inviscid fluid in the absence of mean flow. The study shows in particular how the reflection and transmission coefficients of an acoustic plane wave produced by such a device can be expressed in terms of the Rayleigh conductivity of an isolated perforation by extending the approach introduced for the case of thick plates by Leppington and Levine, \textit{Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures}, J. Fluid Mech., 1973, p.109-127. Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by reasoning based on physical observation. The paper addresses a mathematical justification of these approaches, yielding accurate bounds for various geometries, untilted or tilted, with a conical shape or an elliptical section. Accurate estimates of the Rayleigh conductivity for a single perforation have a direct impact on the precision of models used for predicting the acoustic behavior of a perforated plate mainly on the basis of its reflection and transmission coefficients. It is shown in this paper how asymptotic expansions can be used to derive first and second-order accurate, albeit approximate expressions of these coefficients, as well as of the effective compliance of the perforated plate

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases