A modal synthesis method for the elastoacoustic vibration problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 121-142.

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved, error estimates are given, and numerical experiments exhibiting the good performance of the method are reported.

DOI : 10.1051/m2an:2002005
Classification : 65N15, 65N25, 74F10
Mots-clés : fluid-structure interaction, elastoacoustic, modal synthesis 
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     title = {A modal synthesis method for the elastoacoustic vibration problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {121--142},
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Bermúdez, Alfredo; Hervella-Nieto, Luis; Rodríguez, Rodolfo. A modal synthesis method for the elastoacoustic vibration problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 121-142. doi : 10.1051/m2an:2002005. http://www.numdam.org/articles/10.1051/m2an:2002005/

[1] I. Babuška and J. Osborn, Eigenvalue problems. In Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions, Eds., North Holland, Amsterdam (1991). | MR | Zbl

[2] A. Bermúdez, P. Gamallo, L. Hervella-Nieto and R. Rodríguez, Finite element analysis of the elastoacoustic problem using the pressure in the fluid. Preprint DIM 2001-05, Universidad de Concepción, Concepción, Chile (submitted). | Zbl

[3] F. Bourquin, Analysis and comparison of several component mode synthesis methods on one-dimensional domains. Numer. Math. 58 (1990) 11-34. | EuDML | Zbl

[4] F. Bourquin, Component mode synthesis and eigenvales of second order operators: Discretization and algorithm. RAIRO Modél. Math. Anal. Numér. 26 (1992) 385-423. | EuDML | Numdam | Zbl

[5] F. Bourquin, A pure displacement dynamic substructuring method with accurate pressure for elastoacoustics. Laboratoire Central des Ponts et Chaussées, R/94/05/7 (1994).

[6] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). | MR | Zbl

[7] R. Craig and M.C.C. Bampton, Coupling of substructures for dynamic analysis. AIAA J. 6 (1968) 1313-1321. | Zbl

[8] R.L. Goldman, Vibration analysis of dynamic analysis. AIAA J. 7 (1969) 1152-1154. | Zbl

[9] P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). | MR | Zbl

[10] P. Grisvard, Caractérisation de quelques espaces d'interpolation. Arch. Rat. Mech. Anal. 25 (1967) 40-63. | Zbl

[11] L. Hervella-Nieto, Métodos de elementos finitos y reducción modal para problemas de interacción fluido-estructura. Ph.D. thesis, Publicaciones del Departamento de Matemática Aplicada, 27, Universidad de Santiago de Compostela (2000).

[12] W.C. Hurty, Dynamic analysis of structural systems using component modes. AIAA J. 4 (1965) 678-685.

[13] W.G. Kolata, Approximation in variationally posed eigenvalues problems. Numer. Math. 29 (1978) 159-171. | EuDML | Zbl

[14] J.L. Lions, Théorèmes de trace et d'interpolation (I). Ann. Scuola Norm. Sup. Pisa 13 (1959) 389-403. | EuDML | Numdam | Zbl

[15] H.J.-P. Morand and R. Ohayon, Interactions Fluides-Structure. Masson, Paris (1996). | MR | Zbl

[16] H.J.-P. Morand and R. Ohayon, Substructure variational analysis of the vibration of coupled fluid-structure systems. Finite element results. Internat. J. Numer. Methods Engrg. 14 (1979) 741-755. | Zbl

[17] J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques. Masson, Paris (1967). | MR | Zbl

[18] G. Sandberg, A new strategy for solving fluid-structure problems. Internat. J. Numer. Methods Engrg. 38 (1995) 357-370. | Zbl

[19] J. Wandinger, Analysis of small vibrations of coupled fluid-structure systems. Z. Angew. Math. Mech. 74 (1994) 37-42. | Zbl

[20] J.-L. Zolesio, Interpolation d'espaces de Sobolev avec conditions aux limites de type mêlé. C. R. Acad. Sci. Paris Série A 285 (1982) 621-624. | Zbl

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