Nombres d'ondes, masses volumiques et modules effectifs de milieux composites formés d'une matrice poro-élastique contenant des inclusions de forme cylindrique

Abstract : We study the propagation of acoustic waves in a porous medium obeying the Biot theory and containing a random distribution of cylindrical cavities and that of an acoustic wave in a fluid containing a random polydisperse distribution of porous spheres. In the first case we use the generalization by Conoir-Norris of the Linton-Martin formula. It allows to take into account the phenomenon of the conversion between the three waves (two longitudinal and one transverse) naturally propagating in a porous Biot medium containing a random distribution of cavities. Analytical expressions are found for the effective wavenumbers of coherent waves in the Rayleigh limit (low frequency regime). The approximations of the densities and heterogeneous media modules are presented up to the order of c2 in concentration. The limiting case of random fluid cavities in an elastic matrix is also discussed. In the second case the effective wavenumbers, moduli and density are determined for polydisperse distributions of poroelastic spheres. To achieve this, the recent formulas of the effective wave number given by Linton and Martin in the dilute monodisperse case have been modified. Given the uncertainty for predicting the distribution in size of obstacles, three different probability densities are studied and compared: uniform, Schulz and lognormal. More precisely, the Rayleigh limit is taken into account when the wave lengths can be assumed to be very large compared to the size of the obstacles. Within this limit, simplified formulas for concentrations are provided depending on the parameter characterizing the size dispersion.
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Dossou Gnadjro. Nombres d'ondes, masses volumiques et modules effectifs de milieux composites formés d'une matrice poro-élastique contenant des inclusions de forme cylindrique. Mécanique [physics]. Normandie Université; Université de Lomé (Togo), 2019. Français. ⟨NNT : 2019NORMLH16⟩. ⟨tel-02313683⟩

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