Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-02T23:06:40.832Z Has data issue: false hasContentIssue false
  • English
  • Français

A modal synthesis method for the elastoacoustic vibrationproblem

Published online by Cambridge University Press:  15 April 2002

Alfredo Bermúdez ,
Luis Hervella-Nieto  and
Rodolfo Rodríguez
Alfredo Bermúdez
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain. [email protected].. Partially supported by research project PGIDT00PXI20701PR. Xunta de Galicia (Spain).
Luis Hervella-Nieto
Affiliation:
Departamento de Matemáticas, Universidade da Coruña, 15071 A Coruña, Spain. Partially supported by FONDAP in Applied Mathematics, Chile.
Rodolfo Rodríguez
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160–C, Concepción, Chile. Partially supported by FONDECYT Grant 1.990.346 and FONDAP in Applied Mathematics, Chile.
Get access

Abstract

A modal synthesis method to solve the elastoacoustic vibration problemis 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.

Keywords

Fluid-structure interactionelastoacousticmodal synthesis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 1 , January 2002 , pp. 121 - 142
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

I. Babuska and J. Osborn, Eigenvalue problems. In Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions, Eds., North Holland, Amsterdam (1991).
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).
Bourquin, F., Analysis and comparison of several component mode synthesis methods on one-dimensional domains. Numer. Math. 58 (1990) 11-34. CrossRef
Bourquin, F., Component mode synthesis and eigenvales of second order operators: Discretization and algorithm. RAIRO Modél. Math. Anal. Numér. 26 (1992) 385-423. CrossRef
F. Bourquin, A pure displacement dynamic substructuring method with accurate pressure for elastoacoustics. Laboratoire Central des Ponts et Chaussées, R/94/05/7 (1994).
P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
Craig, R. and Bampton, M.C.C., Coupling of substructures for dynamic analysis. AIAA J. 6 (1968) 1313-1321.
Goldman, R.L., Vibration analysis of dynamic analysis. AIAA J. 7 (1969) 1152-1154. CrossRef
P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).
Grisvard, P., Caractérisation de quelques espaces d'interpolation. Arch. Rat. Mech. Anal. 25 (1967) 40-63. CrossRef
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).
Hurty, W.C., Dynamic analysis of structural systems using component modes. AIAA J. 4 (1965) 678-685. CrossRef
Kolata, W.G., Approximation in variationally posed eigenvalues problems. Numer. Math. 29 (1978) 159-171. CrossRef
Lions, J.L., Théorèmes de trace et d'interpolation (I). Ann. Scuola Norm. Sup. Pisa 13 (1959) 389-403.
H.J.-P. Morand and R. Ohayon, Interactions Fluides-Structure. Masson, Paris (1996).
Morand, H.J.-P. and Ohayon, R., Substructure variational analysis of the vibration of coupled fluid-structure systems. Finite element results. Internat. J. Numer. Methods Engrg. 14 (1979) 741-755. CrossRef
J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques. Masson, Paris (1967).
Sandberg, G., A new strategy for solving fluid-structure problems. Internat. J. Numer. Methods Engrg. 38 (1995) 357-370. CrossRef
Wandinger, J., Analysis of small vibrations of coupled fluid-structure systems. Z. Angew. Math. Mech. 74 (1994) 37-42. CrossRef
Zolesio, J.-L., Interpolation d'espaces de Sobolev avec conditions aux limites de type mêlé. C. R. Acad. Sci. Paris Série A 285 (1982) 621-624.