Finite element analysis of sloshing and hydroelastic vibrations under gravity

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 2, 1999, Pages 305-327

  Bermúdez, Alfredo ^a   Rodríguez, Rodolfo ^b  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b UNIVERSITY OF CONCEPCIÓN   (Chile)

Author keywords

Finite elements; Fluid structure; Hydroelasticity under gravity; Spectral problems; Spurious modes; Vibrations

Indexed keywords

EID: 0040942653     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999117     Document Type: Article

References (21)

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).
2. H. Berger, J. Boujot and R. Ohayon, On a spectral problem in vibration mechanics: computation of elastic tanks partially filled with liquids. J. Math. Anal. Appl. 51 (1975) 272-298.
3. A. Bermúdez, R. Durán, M.A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM J. Numer. Anal. 32 (1995) 1280-1295.
4. A. Bermúdez, R. Durán and R. Rodríguez, Finite element analysis of compressible and incompressible fluid-soud systems. Math. Comp. 67 (1998) 111-136.
5. A. Bermúdez and R. Rodríguez, Finite element computation of the vibration modes of a fluid-solid system. Comp. Methods Appl. Mech. Eng. 119 (1994) 355-370.
6. J. Boujot, Sur l'analyse des caractéristiques vibratoirs d'un liquide contenu dans un reservoir. J. Mécanique 11 (1972) 647-671.
7. J. Boujot, Mathematical formulation of fluid-structure interaction problems. RAIRO Modél. Math. Anal. Numér. 21 (1987) 239-260.
8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991).
9. P. Clement, Approximation by finite element functions using local regularization. RAJRO Anal. Numér. 9 (1975) 77-84.
10. C. Conca, J. Planchard and M. Vanninathan, Fluids and Periodic Structures. Masson, Paris (1992).
11. J. Descloux, N. Nassif and J. Rappaz, On spectral approximation. Part I: The problem of convergence. Part 2: Error estimates for the Galerkin methods. RAIRO Anal. Numér. 12 (1978) 97-119.
12. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1986).
13. P. Grisvard, Elliptic Problems for Non-smooth Domains. Pitman, Boston (1985).
14. T. Kato, Perturbation Theory for Linear Operators. Springer Verlag, Berlin (1966).
15. M. Hamdi, Y. Ouset and G. Verchery, A displacement method for the analysis of vibrations of coupled fluid-structure systems, Internat. J. Numer. Methods Eng. 13 (1978) 139-150.
16. J. Mandel, Cours de Mécanique des Milieux Continus. Gauthier-Villars, Paris (1966).
17. H.J-P. Morand and R. Ohayon, Interactions Fluides-Structures, Recherches en Mathématiques Appliquées. Masson, Paris 23 (1992).
18. R. Rodríguez and J. Solomin, The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. Math. Comp. 65 (1996) 1463-1475.
19. R.M.S.M. Schulkes, Interactions of an elastic solid with a viscous fluid: eigenmode analysis. J. Comput. Phys. 100 (1992) 270-283.
20. P.A. Raviart and J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics. Springer Verlag, Berlin, Heidelberg, New York 606 (1977) 292-315.
21. P. Tong, Liquid sloshing in an elastic container. AFOSR 66-0943, California Institute of Technology, Pasadena, CA (1966).