.. Discrétisation-spatiale, 100 8.1.2 Interpolation géométrique, p.101

H. N. Abramson, The dynamic behaviour of liquids in moving containers. NASA SP-106, 1966.

M. Amabili, M. P. Païdoussis, and A. A. Lakis, VIBRATIONS OF PARTIALLY FILLED CYLINDRICAL TANKS WITH RING-STIFFENERS AND FLEXIBLE BOTTOM, Journal of Sound and Vibration, vol.213, issue.2, pp.259-299, 1998.
DOI : 10.1006/jsvi.1997.1481

O. Andrianarison, Modélisation mécanique et numérique des interactions gravité/compressibilité dans les vibrations de structures couplées à des fluides internes

O. Andrianarison and R. Ohayon, Linear vibrations of a fluid contained in a tank, with compressibility and gravity effects, Proc. of the European Conference on Computational Mechanics, 1999.

O. Andrianarison and R. Ohayon, Gravity-compressibility interaction effects in internal liquidstructure vibrations. Variational formulations, Proc. of the Sixth U.S. National Congress on Computational Mechanics, 2001.

F. Axisa, Modélisation des systèmes mécaniques Interactions fluide-structure, 2001.

I. Babu?-ska, F. Ihlenburg, E. Paik, and S. Sauter, A generalized finite element method for solving the Helmoltz equation in two dimensions with minimal pollution, Comp. Methods in Applied Mech. and Engr, vol.128, pp.3-4325, 1995.

K. Bathe, Finite Element Procedures in Engineering Analysis, Journal of Pressure Vessel Technology, vol.106, issue.4, 1982.
DOI : 10.1115/1.3264375

H. F. Bauer, LIQUID SLOSHING IN A CYLINDRICAL QUARTER TANK, AIAA Journal, vol.1, issue.11, pp.2601-2606, 1963.
DOI : 10.2514/3.2118

H. F. Bauer and M. Chiba, VISCOUS HYDROELASTIC VIBRATIONS IN A CYLINDRICAL CONTAINER WITH AN ELASTIC BOTTOM, Journal of Sound and Vibration, vol.247, issue.1, pp.33-57, 2001.
DOI : 10.1006/jsvi.2001.3633

H. F. Bauer and W. Eidel, Free oscillations and response of a viscous liquid in a rigid circular cylindrical tank, Aerospace Science and Technology, vol.3, issue.8, pp.495-512, 1999.
DOI : 10.1016/S1270-9638(99)00110-8

H. F. Bauer and W. Eidel, Frictionless liquid sloshing in circular cylindrical container configurations, Aerospace Science and Technology, vol.3, issue.5, pp.301-311, 1999.
DOI : 10.1016/S1270-9638(00)86966-7

T. Belytschko, Methods and programs for analysis of fluid-structure systems, Nuclear Engineering and Design, vol.42, issue.1, pp.41-52, 1977.
DOI : 10.1016/0029-5493(77)90060-7

T. Belytschko and W. K. Liu, Computer methods for transient fluid-structure analysis of nuclear reactors, Nuclear Safety, vol.26, pp.14-31, 1985.

T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Element Analysis for Continua and Structures, 2000.

H. Berger, J. Boujot, and R. Ohayon, On a spectral problem in vibration mechanics: Computation of elastic tanks partially filled with liquids, Journal of Mathematical Analysis and Applications, vol.51, issue.2, pp.272-298, 1975.
DOI : 10.1016/0022-247X(75)90123-7

A. Bermúdez, R. Durán, and R. Rodríguez, FINITE ELEMENT SOLUTION OF INCOMPRESSIBLE FLUID-STRUCTURE VIBRATION PROBLEMS, International Journal for Numerical Methods in Engineering, vol.32, issue.8, pp.1435-1448, 1997.
DOI : 10.1002/(SICI)1097-0207(19970430)40:8<1435::AID-NME119>3.0.CO;2-P

A. Bermúdez and R. Rodríguez, Finite element analysis of sloshing and hydroelastic vibrations under gravity. Mathematical modelling and numerical analysis, pp.305-327, 1999.

A. Bermúdez, R. Rodríguez, and D. Santamarina, A finite element solution of an added mass formulation for coupled fluid-solid vibrations, Numerische Mathematik, vol.87, issue.2, pp.201-227, 2000.
DOI : 10.1007/s002110000175

R. E. Bishop and W. G. Price, Hydroelasticity of ships, 1979.

J. Bonet and R. D. Wood, Nonlinear continuum mechanics for finite element analysis, 1997.
DOI : 10.1017/CBO9780511755446

D. E. Bourne and P. C. Kendall, Vector Analysis and Cartesian Tensors, 1977.
DOI : 10.1007/978-1-4899-4427-6

V. A. Buzhinskii, Vortex damping of sloshing in tanks with baffles, Journal of Applied Mathematics and Mechanics, vol.62, issue.2, pp.217-224, 1998.
DOI : 10.1016/S0021-8928(98)00028-8

H. Cartan, Calcul Différentiel, 1967.

X. Chai, Influence de la gravité sur les interactions fluide-structure pour un fluide dans un domaine borné à surface libre, 1996.

X. Chai, J. Genevaux, and J. Brancher, Gravity effects on the coupled frequencies of a 2D fluid-structure problem with a free surface, Journal of Sound and Vibration, vol.215, issue.2, pp.331-342, 1998.

E. R. Christensen, Effect of pressure stiffness on the dynamics of solid rocket motors, Journal of Guidance, Control, and Dynamics, vol.17, issue.1, pp.62-68, 1994.
DOI : 10.2514/3.21159

E. R. Christensen, Vibration analysis of fluid-structure systems in the space shuttle main engine, Proc. of the 35th Structures, Structural Dynamics, and Materials Conference, pp.94-1643, 1994.

B. Christophe and N. Piet-lahanier, Flexible launcher dynamics prevision, Proc. of the 45 th Congress of the International Astronautical Federation, 1994.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1979.

A. Combescure, R. J. Gibert, F. Jeanpierre, A. Hoffmann, and M. Livolant, Fluid-structure interaction: A general method used in the ceasemt computer programs, Computers & Structures, vol.12, issue.4, pp.471-474, 1980.
DOI : 10.1016/0045-7949(80)90122-4

R. N. Coppolino, A numerical efficient finite element hydroelastic analysis. NASA CR-2662, 1976.

R. R. Craig and M. C. Bampton, Coupling of substructures for dynamic analyses, A.I.A.A. Journal, vol.6, issue.7, pp.1313-1319, 1968.

R. Dautray and J. Lions, Analyse mathématique et calcul numérique, pour les sciences et les techniques, 1987.

E. De-langre, Fluides et Solides, 2001.

E. De-langre and O. Doaré, Flow-induced bending instabilities of long fluid-conveying risers, Proc. of the Euromech 398 colloquium, 1999.

J. F. Debongnie, On a purely lagrangian formulation of sloshing and fluid-induced vibrations of tanks, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.1, pp.1-18, 1986.
DOI : 10.1016/0045-7825(86)90075-7

W. Ding and Q. Zeng, Identification in frequency domain for dynamic parameters of pendulum model of sloshing liquid, Journal of Vibration Engineering, vol.5, issue.3, pp.211-218, 1992.

M. P. Païdoussis, Fluid-Structure Interactions : Slender Structures and Axial flow, 1998.
DOI : 10.1017/CBO9780511760792

S. Dutta and M. K. Laha, Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low-order boundary element method, International Journal for Numerical Methods in Engineering, vol.27, issue.9, pp.1633-1648, 2000.
DOI : 10.1002/(SICI)1097-0207(20000330)47:9<1633::AID-NME851>3.0.CO;2-1

O. M. Faltinsen and O. F. Rognebakke, Sloshing and slamming in tanks, Proc. of Hydronav'99 and Manouevring'99, 1999.

M. F. Fisher, G. R. Schmidt, and J. J. Martin, Analysis of cryogenic propellant behavior in microgravity and low thrust environments, 27th Joint Propulsion Conference, 1991.
DOI : 10.2514/6.1991-2173

M. Géradin and D. Rixen, Mechanical Vibrations : Theory and Applications to Structural Dynamics, 1997.

V. Gorge, Modélisation des vibrations de coques axisymétriques intelligentes contenant un fluide acoustique, 2001.

E. W. Graham, The characteristics of fuel motion which affect airplane dynamics, 1951.

H. P. Greenspan, The theory of rotating fluids, 1986.

R. J. Hansman, Low gravity fluid measurement and fluid structure interactions, Proc. of the In-Space Research, 1985.

H. D. Hibbitt, Some follower forces and load stiffness, International Journal for Numerical Methods in Engineering, vol.10, issue.6, pp.937-941, 1979.
DOI : 10.1002/nme.1620140613

J. , S. Hubert, and E. Sanchez-palencia, Vibration and coupling of continuous systems ? Asymptotic methods, 1989.

T. J. Hughes, The Finite Element Method, 1987.

F. Ihlenburg, Finite Element Analysis of Acoustic Scattering, 1998.
DOI : 10.1007/b98828

P. and M. Iver, Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth, J. Fluid Mech, vol.201, pp.243-257, 1989.

M. C. Junger and D. Feit, Sound, structures and their interaction, 1993.

L. Kiefling and G. C. Feng, Fluid-Structure Finite Element Vibrational Analysis, AIAA Journal, vol.14, issue.2, pp.199-203, 1976.
DOI : 10.2514/3.61357

M. C. Kim, S. S. Lee, and A. M. Kabe, An analytical study of area formulations in fluid-structure interaction, 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, pp.2001-2011, 1998.
DOI : 10.2514/6.1998-1948

M. C. Kim and S. S. Lee, Hydroelastic analysis of a rectangular tank, Proc. of MSC 1997 Aerospace Users' Conference, 1997.

M. Klein, S. M. Niku, R. A. Adey, and A. Kreis, Analysis of the behaviour of liquid filled tanks by coupling boundary element and finite element methods

E. Kock and L. Olson, Fluid-structure interaction analysis by the finite element method-a variational approach, International Journal for Numerical Methods in Engineering, vol.21, issue.3, pp.463-491, 1991.
DOI : 10.1002/nme.1620310305

A. Kreis and M. Klein, On the analysis of liquid filled free-free tanks, Proc. of International Conference : Spacecraft Structures and Mechanical Testing, pp.437-442, 1991.

A. Kreis and M. Klein, On the analysis of free-free prestressed structures, Proc. of the International FEM'92 Congress, pp.265-278, 1992.

L. Landau and E. Lifchitz, Physique Théorique, Mécanique des Fluides. Editions de Moscou, 1971.

S. S. Lee, M. C. Kim, and D. R. Williamson, Implementation of a fluid-structure interaction formulation using MSC/NASTRAN, Proc. of MSC 1997 Aerospace Users' Conference, 1997.

A. W. Leissa, Vibration of Shells. NASA SP-288, 1973.

C. Lesueur, Rayonnement acoustique des structures ? Vibroacoustique, interactions fluidestructure, Editions Eyrolles, 1988.

J. L. Liow, Boundary integral method for slosh simulation, Proc. of the 6th Asian Congress of Fluid Mechanics, pp.1524-1527, 1995.

W. K. Liu and D. C. Ma, Coupling effect between liquid sloshing and flexible fluid-filled systems, Nuclear Engineering and Design, vol.72, issue.3, pp.345-357, 1982.
DOI : 10.1016/0029-5493(82)90048-6

W. K. Liu and R. A. Uras, Variational approach to fluid-structure interaction with sloshing, Nuclear Engineering and Design, vol.106, issue.1, pp.69-85, 1988.
DOI : 10.1016/0029-5493(88)90270-1

J. Mandel, Cours de Mécanique des Milieux Continus, 1966.

Y. Mauriot, G. Ordonneau, and N. Piet, Use of an elastic-acoustic element for Pogo stability analysis of the Ariane 5 upper stage, Proc. of the Launch Vehicle Vibrations, First European conference on Launcher Technology. CNES Toulouse (France), 1999.

J. W. Miles, On the sloshing of a liquid in a flexible tank, 1958.

J. W. Miles and B. A. Troesch, Surface Oscillations of a Rotating Liquid, Journal of Applied Mechanics, vol.28, issue.4, 1961.
DOI : 10.1115/1.3641773

P. Mohan, Development and applications of a flat triangular element for thin laminated shells, 1997.

N. N. Moïseyev and V. V. Rumyantsev, Dynamic stability of bodies containing fluid, 1968.
DOI : 10.1007/978-3-642-86452-0

H. J. and -. Morand, Vibrations en vol des lanceurs à liquides : formulation variationnelle symétrique complète, Calcul des Structures et Intelligence Artificielle, 1987.

H. J. , -. Morand, and R. Ohayon, Internal pressure effects on the vibration of partially filled elastic tanks, Proc. of the World Congress on Application of Finite Element Methods to Structural Mechanics, pp.1975-66

H. J. , -. Morand, and R. Ohayon, Interactions Fluides-Structures, Collection RMA P.G. Ciarlet et J.L. Lions, 1992.

H. J. , -. Morand, and R. Ohayon, Fluid-Structure Interactions, 1995.

G. D. Mortchéléwicz, Flutter simulations, Aerospace Science and Technology, vol.4, issue.1, pp.33-40, 2000.
DOI : 10.1016/S1270-9638(00)00116-4

T. Nakayama and K. Washizu, Nonlinear analysis of liquid motion in a container subjected to forced pitching oscillation, Computational Methods in Applied Mechanics and Engineering special issue on Advanced Numerical Method for Fluid-Structure Interaction and Coupled Problems, pp.1207-1220, 1980.
DOI : 10.1002/nme.1620150808

R. Ohayon and C. A. Felippa, The Effect of Wall Motions on the Governing Equations of Contained Fluids, Journal of Applied Mechanics, vol.57, issue.3, pp.783-785, 1990.
DOI : 10.1115/1.2897093

R. Ohayon and H. Morand, Mechanical and numerical modelling of fluid-structure vibration instabilities of liquid propelled launch vehicle, Chaos, Solitons & Fractals, vol.5, issue.9, pp.1705-1724, 1995.
DOI : 10.1016/0960-0779(94)00172-M

R. Ohayon and B. Nicolas-vullierme, An efficient shell element for the computation of the vibrations of fluid-structure systems of revolution, Proc. of the SMIRT-6 Conference, 1981.

R. Ohayon, R. Sampaio, and C. Soize, Dynamic Substructuring of Damped Structures Using Singular Value Decomposition, Journal of Applied Mechanics, vol.64, issue.2, pp.292-298, 1997.
DOI : 10.1115/1.2787306

URL : https://hal.archives-ouvertes.fr/hal-00770023

R. Ohayon and C. Soize, Structural Acoustics and Vibration ? Mechanical models, variational formulations and discretization, 1998.

R. Ohayon and R. Valid, True symmetric variational formulations for fluid-structure interaction in bounded domains -finite element results, Numerical Methods in Coupled Systems, 1984.

L. Olson and T. Vandini, Eigenproblems from finite element analysis of fluid-structure interactions, Computers & Structures, vol.33, issue.3, pp.679-687, 1989.
DOI : 10.1016/0045-7949(89)90242-3

K. C. Park, C. A. Felippa, and R. Ohayon, Partitioned formulation of internal fluid???structure interaction problems by localized Lagrange multipliers, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.24-25, pp.2989-3007, 2001.
DOI : 10.1016/S0045-7825(00)00378-9

I. M. Rapoport, Dynamics of Elastic Containers Partially Filled with Liquids, 1968.

P. Raviart and J. M. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles, 1982.

A. Rittweger, R. Gajdacz, and S. Dieker, The influence of compressibility on the dynamic behaviour of the ESC-tanks, Proc. of the Launch Vehicle Vibrations, First European conference on Launcher Technology. CNES Toulouse (France), 1999.

O. F. Rognebakke and O. M. Faltinsen, Damping of sloshing due to tank roof impact, Proc. of the 15th International Workshop on Water Waves and Floating Bodies, 2000.

P. Ryan, Eigenvalue and eigenfunction error estimates for finite element formulations of sloshstructure interaction, 1998.

C. Saravanan, N. Ganesan, and V. Ramamurti, Study on energy dissipation pattern in vibrating fluid filled cylindrical shells with a constrained viscoelastic layer, Computers & Structures, vol.75, issue.6, pp.575-591, 2000.
DOI : 10.1016/S0045-7949(99)00114-5

J. Schotté and R. Ohayon, Vibration analysis of elastic tanks partially filled with incompressible liquids in presence of a gravity field, Proc. of the Launch Vehicle Vibrations, First European conference on Launcher Technology. CNES Toulouse (France), 1999.

J. Schotté and R. Ohayon, Couplage structure-fluide interne en présence de la gravité, Actes du 5ème Colloque National en Calcul des Structures, pp.311-317

J. Schotté and R. Ohayon, Interactions between sloshing modes and incompressible hydroelastic modes for internal fluid-structure systems, Proc. of the First MIT Conference on Computational Fluid and Solid Mechanics, 2001.
DOI : 10.1016/B978-008043944-0/50813-1

J. Schotté and R. Ohayon, Effect of Gravity on a Free-Free Fluid-Structure System, 5th International Symposium on Fluid Structure International, Aeroeslasticity, and Flow Induced Vibration and Noise, 2002.
DOI : 10.1115/IMECE2002-32868

J. Schotté and R. Ohayon, Vibration analysis of elastic tanks partially filled with incompressible liquids in presence of a gravity field, Int. J. Num. Meth. Eng

R. M. Schulkes and C. Cuvelier, On the computation of normal modes of a rotating, viscous, incompressible fluid with a capillary free boundary, Computer Methods in Applied Mechanics and Engineering, vol.92, issue.1, pp.97-120, 1991.
DOI : 10.1016/0045-7825(91)90200-P

C. C. Smith, The effect of fuel sloshing on the lateral stability of a free-flying airplane model, 1948.

P. and L. Tallec, Introduction à la dynamique des structures, Ellipses, 2000.

P. Tong, Liquid sloshing in an elastic container, Cal. Tech, 1966.

B. Valette, About the influence of pre-stress upon adiabatic perturbations of the Earth, Geophysical Journal International, vol.85, issue.1, pp.179-208, 1986.
DOI : 10.1111/j.1365-246X.1986.tb05177.x

R. Valid, R. Ohayon, and H. Berger, Le calcul des réservoirs élastiques partiellement remplis de liquides pour la prévision de l'effet pogo, Actes du 23ème Congrès de la Fédération Internationale d'Astronautique, 1972.

O. C. Zienkiewicz and P. Bettess, Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment, International Journal for Numerical Methods in Engineering, vol.11, issue.1, pp.1-17, 1978.
DOI : 10.1002/nme.1620130102

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 2000.

.. D. Exemple-d-'un-système-À-deux-d, 167 B.2.1 Cas statique, p.169

.. Variation-de-volume-au-second-ordre, 179 C.2.1 Première méthode, p.180

D. Sommaire and .. Propriétes-de-l-'opérateur-trace, 186 D.2 Formules d'analyse vectorielle 186 D.2.1 Equivalent matriciel du produit vectoriel : matrice spin, p.187

V. Changements-de, 188 D.3.1 Dans les intégrales de volume, p.188