[Reconstruction des trois constants mécaniques matériels d'un cylindre fluide dissipatif à partir de champs acoustiques basses fréquences]
Le problème inverse de milieu pour un domaine cylindrique circulaire est étudié en employant des ondes acoustiques comme rayonnement d'interrogation. Au second ordre en k0a (k0 le nombre d'onde dans le milieu-hôte et a le rayon du cylindre), seuls les trois premiers termes (i.e., les ordres 0, −1 and +1) dans le développement en ondes partielles du champ diffracté sont non-nuls. Ce fait permet d'exprimer le champ diffracté de manière algébrique en fonction des paramètres matériels que sont la densité ρ1 et les parties réelle et imaginaire de la compressibilité complexe κ1 du cylindre. On montre que ces relations peuvent être inversées afin de donner lieu à des expressions explicites et découplées pour ρ1 and κ1 en fonction de la totalité du champ diffracté en zone lointaine. Ces expressions fournissent des estimations précises des paramètres matériels à condition que la fréquence de sondage soit basse et le rayon du cylindre soit connu très précisément.
The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. To second order in k0a (k0 the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, −1 and +1) in the partial wave representation of the scattered field are non-vanishing. This enables the scattered field to be expressed algebraically in terms of the unknown material constants, i.e., the density ρ1, and the real and imaginary parts of complex compressibility κ1 of the cylinder. It is shown that these relations can be inverted to yield explicit, decoupled expressions for ρ1 and κ1 in terms of the totality of the far-zone scattered field. These expressions furnish accurate estimations of the material parameters provided the probe frequency is low and the radius of the cylinder is known very precisely.
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Mot clés : Acoustique, Problème inverse de milieu
@article{CRMECA_2004__332_9_717_0,
author = {Thierry Scotti and Armand Wirgin},
title = {Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields},
journal = {Comptes Rendus. M\'ecanique},
pages = {717--724},
publisher = {Elsevier},
volume = {332},
number = {9},
year = {2004},
doi = {10.1016/j.crme.2004.03.018},
language = {en},
}
TY - JOUR AU - Thierry Scotti AU - Armand Wirgin TI - Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields JO - Comptes Rendus. Mécanique PY - 2004 SP - 717 EP - 724 VL - 332 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2004.03.018 LA - en ID - CRMECA_2004__332_9_717_0 ER -
%0 Journal Article %A Thierry Scotti %A Armand Wirgin %T Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields %J Comptes Rendus. Mécanique %D 2004 %P 717-724 %V 332 %N 9 %I Elsevier %R 10.1016/j.crme.2004.03.018 %G en %F CRMECA_2004__332_9_717_0
Thierry Scotti; Armand Wirgin. Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields. Comptes Rendus. Mécanique, Volume 332 (2004) no. 9, pp. 717-724. doi : 10.1016/j.crme.2004.03.018. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.018/
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