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.
Accepté le :
Publié le :
@article{CRMECA_2017__345_2_130_0,
author = {Bertille Claude and Laetitia Duigou and Gregory Girault and Jean-Marc Cadou},
title = {Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method},
journal = {Comptes Rendus. M\'ecanique},
pages = {130--136},
publisher = {Elsevier},
volume = {345},
number = {2},
year = {2017},
doi = {10.1016/j.crme.2016.11.002},
language = {en},
}
TY - JOUR AU - Bertille Claude AU - Laetitia Duigou AU - Gregory Girault AU - Jean-Marc Cadou TI - Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method JO - Comptes Rendus. Mécanique PY - 2017 SP - 130 EP - 136 VL - 345 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2016.11.002 LA - en ID - CRMECA_2017__345_2_130_0 ER -
%0 Journal Article %A Bertille Claude %A Laetitia Duigou %A Gregory Girault %A Jean-Marc Cadou %T Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method %J Comptes Rendus. Mécanique %D 2017 %P 130-136 %V 345 %N 2 %I Elsevier %R 10.1016/j.crme.2016.11.002 %G en %F CRMECA_2017__345_2_130_0
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] 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: Colloque national en calcul des structures, CSMA, Giens, France, 21–25 May 2007.
[3] Padé approximants, Encycl. Math. Appl., Cambridge University Press, Cambridge, UK, 1996
[4] A critical review of asymptotic numerical methods, Arch. Comput. Methods Eng., Volume 5 (1998), pp. 3-22
[5] A numerical continuation method based on Padé approximants, Int. J. Solids Struct., Volume 37 (2000), pp. 6981-7001
[6] Arpack User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia, 1998
[7] 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] Numerical Recipes in Fortran 77, The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 1992
[9] Computation of Hopf bifurcations coupling reduced order models and the asymptotic numerical method, Comput. Fluids, Volume 76 (2013), pp. 73-85
[10] Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models, Comput. Mech., Volume 47 (2011), pp. 359-377
[11] 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] Vibration and transient response of structural-acoustic interior coupled systems with dissipative interface, Comput. Methods Appl. Mech. Eng., Volume 197 (2008), pp. 4894-4905
Cité par Sources :
Commentaires - Politique