Comptes Rendus
no. 2
Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method
Bertille Claude1; Laetitia Duigou1; Gregory Girault1, 2; Jean-Marc Cadou1 
1 Institut de recherche Dupuy-de-Lôme, FRE CNRS 3744, IRDL, 56100 Lorient, France
2 Centre de recherche des Écoles de Saint-Cyr Coëtquidan, Écoles de Coëtquidan, 56381 Guer cedex, France
Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 130-136.

In this paper, an efficient and robust numerical method is proposed to solve non-symmetric eigenvalue problems resulting from the spatial discretization with the finite element method of a vibroacoustic interior problem. The proposed method relies on a perturbation method. Finding the eigenvalues consists in determining zero values of a scalar that depends on angular frequency. Numerical tests show that the proposed method is not sensitive to poorly conditioned matrices resulting from the displacement–pressure formulation. Moreover, the computational times required with this method are lower than those needed with a classical technique such as, for example, the Arnoldi method.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2016.11.002
Mots-clés : Linear vibroacoustic problem, Eigenvalues, Perturbation method

Bertille Claude 1; Laetitia Duigou 1; Gregory Girault 1, 2; Jean-Marc Cadou 1

1 Institut de recherche Dupuy-de-Lôme, FRE CNRS 3744, IRDL, 56100 Lorient, France
2 Centre de recherche des Écoles de Saint-Cyr Coëtquidan, Écoles de Coëtquidan, 56381 Guer cedex, France 
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Bertille Claude; Laetitia Duigou; Gregory Girault; Jean-Marc Cadou. Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 130-136. doi : 10.1016/j.crme.2016.11.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.11.002/

[1] M. Maess; L. Gaul Substructuring and model reduction of pipe components interacting with acoustic fluids, Mech. Syst. Signal Process., Volume 20 (2006), pp. 45-64

[2] E.H. Boutyour, J.M. Cadou, B. Cochelin, M. Potier-Ferry, Étude des vibrations linéaires de plaques par une méthode asymptotique numérique et les approximants de Padé, in: 8e Colloque national en calcul des structures, CSMA, Giens, France, 21–25 May 2007.

[3] G.A. Baker; P. Graves-Morris Padé approximants, Encycl. Math. Appl., Cambridge University Press, Cambridge, UK, 1996

[4] A. Najah; B. Cochelin; N. Damil; M. Potier-Ferry A critical review of asymptotic numerical methods, Arch. Comput. Methods Eng., Volume 5 (1998), pp. 3-22

[5] A. Elhage-Hussein; M. Potier-Ferry; N. Damil A numerical continuation method based on Padé approximants, Int. J. Solids Struct., Volume 37 (2000), pp. 6981-7001

[6] R. Lehoucq; D.C. Sorensen; C. Yang Arpack User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia, 1998

[7] A. Bermúdez; R. Rodríguez Finite element computation of the vibration modes of a fluid-solid system, Comput. Methods Appl. Mech. Eng., Volume 119 (1994) no. 3–4, pp. 355-370

[8] W.H. Press; S.A. Teukolsky; W.T. Vetterling; B.P. Flannery Numerical Recipes in Fortran 77, The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 1992

[9] J. Heyman; G. Girault; Y. Guevel; C. Allery; A. Hamdouni; J.-M. Cadou Computation of Hopf bifurcations coupling reduced order models and the asymptotic numerical method, Comput. Fluids, Volume 76 (2013), pp. 73-85

[10] F. Boumediene; L. Duigou; E.H. Boutyour; A. Miloudi; J.-M. Cadou Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models, Comput. Mech., Volume 47 (2011), pp. 359-377

[11] A. Bobillot; É. Balmès Iterative techniques for eigenvalue solutions of damped structures coupled with fluids, Proc. 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, The American Institute of Aeronautics and Astronautics, Denver, CO, USA, 2002, p. 1391

[12] J.-F. Deü; W. Larbi; R. Ohayon Vibration and transient response of structural-acoustic interior coupled systems with dissipative interface, Comput. Methods Appl. Mech. Eng., Volume 197 (2008), pp. 4894-4905

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