Comptes Rendus
no. 3
Vibrations of elastic systems with a large number of tiny heavy inclusions
[Vibrations de systèmes élastiques avec un grand nombre de petites inclusions à forte densité]
Volodymyr Rybalko1
1 UFR de mathématiques, case 7012, Université Paris 7, Denis-Diderot, 2, place Jussieu, 75251 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 3, pp. 245-250.

On considère un problème spectral qui modélise les vibrations propres d'un milieu complexe constitué d'un milieu élastique et d'un grand nombre de petites inclusions rigides à forte densité. On étudie le comportement asymptotique de ce problème lorsque le nombre d'inclusions et leur densité tendent vers l'infini. On obtient un problème spectral limite pour une famille rationnelle fractionnaire d'opérateurs qui décrit le comportement macroscopique du système (vibrations globales).

We consider a spectral problem modeling natural vibrations of a complex medium that consists of an elastic medium and tiny rigid inclusions. We study the asymptotic behaviour of solutions of this problem when the total number of inclusions and their density tend to infinity. We obtain a limit problem being a spectral problem for a linear fractional operator pencil that describes the macroscopic behaviour of the system (global vibrations).

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02233-1

Volodymyr Rybalko 1

1 UFR de mathématiques, case 7012, Université Paris 7, Denis-Diderot, 2, place Jussieu, 75251 Paris cedex 05, France 
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Volodymyr Rybalko. Vibrations of elastic systems with a large number of tiny heavy inclusions. Comptes Rendus. Mathématique, Volume 334 (2002) no. 3, pp. 245-250. doi : 10.1016/S1631-073X(02)02233-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02233-1/

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