Un problème Spectral Issu d'un Couplage Elasto-Acoustique

Mario Durán; Jean-Claude Nédélec

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 4, page 835-857
  • ISSN: 0764-583X

Abstract

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We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure. More precisely, we study the existence of solutions for a quadratic eigenvalue problem, which describes the vibrations of a system made up of two elastic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem shall be treated like a generalized eigenvalue problem. Thus by using some functional analysis results, we deduce the existence of solutions and prove a spectral asymptotic behavior property, which allows us to compare the spectrum of this coupled model and the spectrum associated to the problem without transmission between the fluid-solid media.

How to cite

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Durán, Mario, and Nédélec, Jean-Claude. "Un problème Spectral Issu d'un Couplage Elasto-Acoustique." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 835-857. <http://eudml.org/doc/197543>.

@article{Durán2010,
abstract = { We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure. More precisely, we study the existence of solutions for a quadratic eigenvalue problem, which describes the vibrations of a system made up of two elastic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem shall be treated like a generalized eigenvalue problem. Thus by using some functional analysis results, we deduce the existence of solutions and prove a spectral asymptotic behavior property, which allows us to compare the spectrum of this coupled model and the spectrum associated to the problem without transmission between the fluid-solid media. },
author = {Durán, Mario, Nédélec, Jean-Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Couplage élasto-acoustique; problème quadratique de valeurs propres.},
language = {eng},
month = {3},
number = {4},
pages = {835-857},
publisher = {EDP Sciences},
title = {Un problème Spectral Issu d'un Couplage Elasto-Acoustique},
url = {http://eudml.org/doc/197543},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Durán, Mario
AU - Nédélec, Jean-Claude
TI - Un problème Spectral Issu d'un Couplage Elasto-Acoustique
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 835
EP - 857
AB - We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure. More precisely, we study the existence of solutions for a quadratic eigenvalue problem, which describes the vibrations of a system made up of two elastic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem shall be treated like a generalized eigenvalue problem. Thus by using some functional analysis results, we deduce the existence of solutions and prove a spectral asymptotic behavior property, which allows us to compare the spectrum of this coupled model and the spectrum associated to the problem without transmission between the fluid-solid media.
LA - eng
KW - Couplage élasto-acoustique; problème quadratique de valeurs propres.
UR - http://eudml.org/doc/197543
ER -

References

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  2. C. Conca and M. Durán, On some class of elliptic spectral problems. Rapport interne, Facultad de Matemáticas, Universidad Católica de Chile, PUC-FM/99-07 (1999).  
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  5. M. Durán, Étude théorique et numérique de quelques problèmes de type fluide-solide, Partie I. Thèse de doctorat à l'École Polytechnique, Paris (1996).  
  6. M. Durán, Mathematical and numerical analysis of an elastic-acoustic coupling, in Proceeding of Second ECCOMAS Conference on Numerical Methods in Engineering, J. Wiley & Sons Ltd. (1996) 888-893.  
  7. V. Hutson and J.S. Pym, Applications of Functional Analysis and Operator Theory. Academic Press, London (1980).  
  8. T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, Berlin (1976).  
  9. F. Lene and D. Leguillon, Étude de l'influence d'un glissement entre les constituants d'un matériau composite sur ses coefficients de comportements effectifs. J. Mécanique20 (1981) 509-536.  
  10. J. Necas, Les Méthodes Directes en Théorie des Equations Elliptiques. Masson, Paris (1967).  
  11. P.-A. Raviart and J.-M. Thomas, Introduction à l'Analyse Numérique des Equations aux Dérivées Partielles. Masson, Paris (1983).  

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