Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields

Thierry Scotti; Armand Wirgin

doi:10.1016/j.crme.2004.03.018

Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields
[Reconstruction des trois constants mécaniques matériels d'un cylindre fluide dissipatif à partir de champs acoustiques basses fréquences]

Présenté par : Pierre Suquet

Thierry Scotti ¹ ; Armand Wirgin ¹

¹ Laboratoire de mécanique et d'acoustique, UPR 7051 du CNRS, 31, chemin Joseph Aiguier, 13402 Marseille cedex 20, France

Comptes Rendus. Mécanique, Volume 332 (2004) no. 9, pp. 717-724.

Résumé
Abstract

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.

Reçu le : 2003-07-15
Accepté le : 2004-03-30
Publié le : 2004-07-23

DOI : 10.1016/j.crme.2004.03.018

Keywords: Acoustics, Inverse medium problem
Mot clés : Acoustique, Problème inverse de milieu

Affiliations des auteurs :

Thierry Scotti ¹ ; Armand Wirgin ¹

¹ Laboratoire de mécanique et d'acoustique, UPR 7051 du CNRS, 31, chemin Joseph Aiguier, 13402 Marseille cedex 20, France

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     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},
}

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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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