title: The direct and inverse problems of an air-saturated porous cylinder submitted to acoustic radiation.
abstract: Gas-saturated porous skeleton materials such as geomaterials, polymeric and metallic foams, or biomaterials are fundamental in a diverse range of applications, from structural materials to energy technologies. Most polymeric foams are used for noise control applications and knowledge of the manner in which the energy of sound waves is dissipated with respect to the intrinsic acoustic properties is important for the design of sound packages. Foams are often employed in the audible, low frequency range where modeling and measurement techniques for the recovery of physical parameters responsible for energy loss are still few. Accurate acoustic methods of characterization of porous media are based on the measurement of the transmitted and/or reflected acoustic waves by platelike specimens at ultrasonic frequencies. In this study we develop an acoustic method for the recovery of the material parameters of a rigid-frame, air-saturated polymeric foam cylinder. A dispersion relation for sound wave propagation in the porous medium is derived from the propagation equations and a model solution is sought based on plane-wave decomposition using orthogonal cylindrical functions. The explicit analytical solution equation of the scattered field shows that it is also dependent on the intrinsic acoustic parameters of the porous cylinder, namely, porosity, tortuosity, and flow resistivity (permeability). The inverse problem of the recovery of the flow resistivity and porosity is solved by seeking the minima of the objective functions consisting of the sum of squared residuals of the differences between the experimental and theoretical scattered field data.
authors.affiliation: Laboratoire de Mécanique et d'Acoustique, UPR7051 CNRS, 31 chemin Joseph Aiguier, 13402 Marseille Cedex 20, France. ogam@lma.cnrs-mrs.fr
authors.forename: Erick
authors.initials: E
authors.lastname: Ogam
authors.forename: Claude
authors.initials: C
authors.lastname: Depollier
authors.forename: Z E A
authors.initials: ZE
authors.lastname: Fellah