R. Ohayon and C. Soize, Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model, Computational Mechanics, vol.258, issue.2, pp.1071-1078, 2015.
DOI : 10.1007/s00466-014-1091-4

URL : https://hal.archives-ouvertes.fr/hal-01081488

D. Kana, U. Lindholm, and H. Abramson, AN EXPERIMENTAL STUDY OF LIQUID INSTABILITY IN A VIBRATING ELASTIC TANK, Symposium on Structural Dynamics and Aeroelasticity, pp.1183-1188, 1966.
DOI : 10.2514/6.1965-1116

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics, ASCE)
DOI : 10.1061/9780784412237

URL : https://hal.archives-ouvertes.fr/hal-00749201

M. Mignolet and C. Soize, Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.45-48, pp.45-48, 2008.
DOI : 10.1016/j.cma.2008.03.032

URL : https://hal.archives-ouvertes.fr/hal-00686140

R. Ohayon and C. Soize, Advanced Computational Vibroacoustics -Reduced-Order Models and Uncertainty Quantification
URL : https://hal.archives-ouvertes.fr/hal-01162161

P. De-gennes, F. Brochard-wyart, and D. Quéré, Capillarity and Wetting Phenomena. Drops, Bubbles, Pearls, Waves, 2004.

H. Abramson, The dynamic behavior of liquids in moving containers, 1966.

A. Myshkis, V. Babskii, N. Kopachevskii, L. Slobozhanin, A. Tyuptsov et al., Low- Gravity Fluid Mechanics, 1987.
DOI : 10.1007/978-3-642-70964-7

F. Dodge, The New " Dynamical Behaviour of Liquids in Moving Containers, Southwest Research Institute, 2000.

N. Moiseyev and V. Rumyantsev, Dynamic Stability of Bodies Containing Fluid, Applied Physics and Engineering Edition, vol.6, 1968.
DOI : 10.1007/978-3-642-86452-0

R. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, 2005.
DOI : 10.1017/CBO9780511536656

H. Morand and R. Ohayon, Fluid Structure Interaction, 1995.

A. Bermùdez, R. Rodríguez, and D. Santamarina, Finite element computation of sloshing modes in containers with elastic baffle plates, International Journal for Numerical Methods in Engineering, vol.606, issue.3, pp.447-467, 2003.
DOI : 10.1002/nme.578

R. Ohayon, Reduced models for fluid???structure interaction problems, International Journal for Numerical Methods in Engineering, vol.60, issue.1, pp.139-152, 2004.
DOI : 10.1002/nme.957

C. Felippa, K. Park, and M. Ross, A Classification of Interface Treatments for FSI, in Fluid Structure Interaction II, pp.27-51, 2010.
DOI : 10.1007/978-3-642-14206-2_2

C. Farhat, E. Chiu, D. Amsallem, J. Schotté, and R. Ohayon, Modeling of Fuel Sloshing and its Physical Effects on Flutter, AIAA Journal, vol.51, issue.9, pp.2252-2265, 2013.
DOI : 10.2514/1.J052299

J. Schotté and R. Ohayon, Linearized formulation for fluid???structure interaction: Application to the linear dynamic response of a pressurized elastic structure containing a fluid with a free surface, Journal of Sound and Vibration, vol.332, issue.10, pp.2396-2414, 2013.
DOI : 10.1016/j.jsv.2012.07.036

W. Dettmer and D. Peri´cperi´c, A computational framework for free surface fluid flows accounting for surface tension, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.23-24, pp.3038-3071, 2006.
DOI : 10.1016/j.cma.2004.07.057

A. Veldman, J. Gerrits, R. Luppes, J. Helder, and J. Vreeburg, The numerical simulation of liquid sloshing on board spacecraft, Journal of Computational Physics, vol.224, issue.1, pp.82-99, 2007.
DOI : 10.1016/j.jcp.2006.12.020

M. El-kamali, J. Schotté, and R. Ohayon, Three-dimensional modal analysis of sloshing under surface tension, International Journal for Numerical Methods in Fluids, vol.317, issue.022101, pp.87-105, 2011.
DOI : 10.1002/fld.2457

V. Pukhnachev and V. Solonnikov, On the problem of dynamic contact angle, Journal of Applied Mathematics and Mechanics, vol.46, issue.6, pp.961-971, 1982.
DOI : 10.1016/0021-8928(82)90059-4

P. Concus and R. Finn, ON THE BEHAVIOR OF A CAPILLARY SURFACE IN A WEDGE, Proceedings of the National Academy of Sciences, vol.63, issue.2, pp.292-299, 1969.
DOI : 10.1073/pnas.63.2.292

P. Thompson and M. Robbins, Simulations of contact-line motion: Slip and the dynamic contact angle, Physical Review Letters, vol.63, issue.7, pp.766-769, 1989.
DOI : 10.1103/PhysRevLett.63.766

B. Cocciaro, S. Faetti, and M. Nobili, Capillarity effects on surface gravity waves in a cylindrical container: wetting boundary conditions, Journal of Fluid Mechanics, vol.221, issue.-1, pp.325-343, 1991.
DOI : 10.1146/annurev.fl.11.010179.002103

V. Dussan, E. Ramé, and S. Garoff, On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation, Journal of Fluid Mechanics, vol.209, issue.-1, pp.97-111, 1991.
DOI : 10.1017/S0022112076000906

J. Keller and G. Merchant, Flexural rigidity of a liquid surface, Journal of Statistical Physics, vol.30, issue.5-6, pp.1039-1051, 1991.
DOI : 10.1007/BF01029998

D. Henderson and J. Miles, Surface-wave damping in a circular cylinder with a fixed contact line, Journal of Fluid Mechanics, vol.94, issue.-1, pp.285-299, 1994.
DOI : 10.1063/1.858472

P. Shankar and R. Kidambi, The contact angle in inviscid fluid mechanics, Proceedings of the Indian Academy of Sciences, pp.227-240, 2005.
DOI : 10.1007/BF02829629

T. Miras, J. Schotté, and R. Ohayon, Energy approach for static and linearized dynamic studies of elastic structures containing incompressible liquids with capillarity: a theoretical formulation, Computational Mechanics, vol.258, issue.6, pp.729-741, 2012.
DOI : 10.1007/s00466-012-0786-7

R. Finn, On the Equations of Capillarity, Journal of Mathematical Fluid Mechanics, vol.3, issue.2, pp.139-151, 2001.
DOI : 10.1007/PL00000966

R. Finn, The contact angle in capillarity, Physics of Fluids, vol.18, issue.4, p.47102, 2006.
DOI : 10.1063/1.2185655

R. Finn and G. Luli, On the Capillary Problem for Compressible Fluids, Journal of Mathematical Fluid Mechanics, vol.9, issue.1, pp.87-103, 2007.
DOI : 10.1007/s00021-005-0203-5

J. Luke, A variational principle for a fluid with a free surface, Journal of Fluid Mechanics, vol.125, issue.02, pp.395-397, 1967.
DOI : 10.1007/BF01449125

J. Miles, Nonlinear surface waves in closed basins, Journal of Fluid Mechanics, vol.8, issue.03, pp.419-448, 1976.
DOI : 10.1063/1.1706491

O. Limarchenko, Effect of capillarity on the dynamics of a container liquid system. Soviet Applied Mechanics, pp.601-604, 1981.

O. Limarchenko, Application of the variational method to the solution of nonlinear problems of the dynamics of combined motions of a tank with fluid. Soviet Applied Mechanics, pp.1021-1025, 1983.

L. Peterson, E. Crawley, and R. Hansman, Nonlinear fluid slosh coupled to the dynamics of a spacecraft, AIAA Journal, vol.27, issue.9, pp.1230-1240, 1989.
DOI : 10.2514/3.10250

I. Harari, K. Grosh, T. Hughes, M. Malhotra, P. Pinsky et al., Recent developments in finite element methods for structural acoustics, Archives of Computational Methods in Engineering, vol.49, issue.4, pp.2-3131, 1996.
DOI : 10.1007/BF03041209

R. Ohayon and C. Soize, Structural Acoustics and Vibration, The Journal of the Acoustical Society of America, vol.109, issue.6, 1998.
DOI : 10.1121/1.1352086

URL : https://hal.archives-ouvertes.fr/hal-00689039

R. Ohayon and C. Soize, Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification, International Journal of Aeronautical and Space Sciences, vol.13, issue.2, pp.127-153, 2012.
DOI : 10.5139/IJASS.2012.13.2.127

URL : https://hal.archives-ouvertes.fr/hal-00713892

C. Soize, Coupling between an undamped linear acoustic fluid and a damped nonlinear structure???Statistical energy analysis considerations, The Journal of the Acoustical Society of America, vol.98, issue.1, pp.373-385, 1995.
DOI : 10.1121/1.413692

URL : https://hal.archives-ouvertes.fr/hal-00770285

T. Tezduyar, M. Behr, and J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces???The deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests, Computer Methods in Applied Mechanics and Engineering, vol.94, issue.3, pp.339-351, 1992.
DOI : 10.1016/0045-7825(92)90059-S

T. Tezduyar, M. Behr, S. Mittal, and J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces???The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders, Computer Methods in Applied Mechanics and Engineering, vol.94, issue.3, pp.353-371, 1992.
DOI : 10.1016/0045-7825(92)90060-W

C. Farhat, M. Lesoinne, M. , L. Tallec, and P. , Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.95-114, 1998.
DOI : 10.1016/S0045-7825(97)00216-8

C. Farhat, P. Geuzaine, and G. Brown, Application of a three-field nonlinear fluid???structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter, Computers & Fluids, vol.32, issue.1, pp.3-29, 2003.
DOI : 10.1016/S0045-7930(01)00104-9

T. Tezduyar, Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.23-24, pp.2983-3000, 2006.
DOI : 10.1016/j.cma.2004.09.018

W. Wall, S. Genkinger, and E. Ramm, A strong coupling partitioned approach for fluid???structure interaction with free surfaces, Computers & Fluids, vol.36, issue.1, pp.169-183, 2007.
DOI : 10.1016/j.compfluid.2005.08.007

Y. Bazilevs, V. Calo, T. Hughes, and Y. Zhang, Isogeometric fluid-structure interaction: theory, algorithms, and computations, Computational Mechanics, vol.196, issue.2, pp.3-37, 2008.
DOI : 10.1007/s00466-008-0315-x

K. Takizawa and T. Tezduyar, Multiscale space???time fluid???structure interaction techniques, Computational Mechanics, vol.31, issue.3, pp.247-267, 2011.
DOI : 10.1007/s00466-011-0571-z

Y. Bazilevs, K. Takizawa, and T. Tezduyar, Computational Fluid-Structure Interaction
DOI : 10.1002/9781118483565

F. Nobile, M. Pozzoli, and C. Vergara, Time accurate partitioned algorithms for the solution of fluid???structure interaction problems in haemodynamics, Computers & Fluids, vol.86, pp.470-482, 2013.
DOI : 10.1016/j.compfluid.2013.07.031

C. Farhat and V. Lakshminarayana, An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid???structure interaction problems, Journal of Computational Physics, vol.263, pp.53-70, 2014.
DOI : 10.1016/j.jcp.2014.01.018

Z. Li, J. Leduc, A. Combescure, and F. Leboeuf, Coupling of SPH-ALE method and finite element method for transient fluid???structure interaction, Computers & Fluids, vol.103, pp.6-17, 2014.
DOI : 10.1016/j.compfluid.2014.06.028

P. Becker, S. Idelsohn, and E. Oñate, A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the Particle Finite Element Method with fixed mesh 2015, pp.1091-1104

J. Cahn and J. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics, vol.28, issue.2, pp.258-267, 1958.
DOI : 10.1063/1.1744102

E. Van-brummelen, M. Shokrpour-roudbari, and G. Van-zwieten, Elasto-capillarity simulations based on the Navier-Stokes-Cahn-Hilliard equations. ArXiv 1510, pp.1-8, 2015.

T. Lieu, C. Farhat, and M. Lesoinne, Reduced-order fluid/structure modeling of a complete aircraft configuration, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.41-43, pp.41-435730, 2006.
DOI : 10.1016/j.cma.2005.08.026

M. Grepl, Y. Maday, N. Nguyen, and A. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.3, pp.575-605, 2007.
DOI : 10.1051/m2an:2007031

URL : https://hal.archives-ouvertes.fr/hal-00112154

N. Nguyen and J. Peraire, An efficient reduced-order modeling approach for non-linear parametrized partial differential equations, International Journal for Numerical Methods in Engineering, vol.41, issue.1, pp.27-55, 2008.
DOI : 10.1002/nme.2309

D. Amsallem, J. Cortial, K. Carlberg, and C. Farhat, A method for interpolating on manifolds structural dynamics reduced-order models, International Journal for Numerical Methods in Engineering, vol.36, issue.11, pp.1241-1258, 2009.
DOI : 10.1002/nme.2681

K. Carlberg, C. Bou-mosleh, and C. Farhat, Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations, International Journal for Numerical Methods in Engineering, vol.35, issue.2, pp.155-181, 2011.
DOI : 10.1002/nme.3050

D. Amsallem, M. Zahr, and C. Farhat, Nonlinear model order reduction based on local reduced-order bases, International Journal for Numerical Methods in Engineering, vol.26, issue.12, pp.891-916, 2012.
DOI : 10.1002/nme.4371

D. Amsallem and C. Farhat, On the stability of projection-based linear reduced-order models: Descriptor vs nondescriptor forms in Reduced Order Methods for Modeling and Computational Reduction, pp.215-234, 2014.

C. Farhat, P. Avery, T. Chapman, and J. Cortial, Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency, International Journal for Numerical Methods in Engineering, vol.92, issue.10, pp.625-662, 2014.
DOI : 10.1002/nme.4668

U. Hetmaniuk, R. Tezaur, and C. Farhat, Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems, International Journal for Numerical Methods in Engineering, vol.51, issue.1, pp.1636-1662, 2012.
DOI : 10.1002/nme.4271

U. Hetmaniuk, R. Tezaur, and C. Farhat, An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems, International Journal for Numerical Methods in Engineering, vol.23, issue.2, pp.1109-1124, 2013.
DOI : 10.1002/nme.4436

T. Bui-thanh, D. Murali, and K. Willcox, Proper Orthogonal Decomposition Extensions for Parametric Applications in Compressible Aerodynamics, 21st AIAA Applied Aerodynamics Conference, 2003.
DOI : 10.2514/6.2003-4213

D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005.
DOI : 10.1016/j.jcp.2004.07.015

D. Amsallem, M. Zahr, Y. Choi, and C. Farhat, Design optimization using hyper-reduced-order models. Structural and Multidisciplinary Optimization 2015, pp.919-940

C. Farhat, T. Chapman, and P. Avery, Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models, International Journal for Numerical Methods in Engineering, vol.32, issue.8, pp.1077-1110, 2015.
DOI : 10.1002/nme.4820

P. Holmes, J. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 1996.

C. Soize, Reduced models in the medium frequency range for general dissipative structural-dynamics systems, European Journal of Mechanics - A/Solids, vol.17, issue.4, pp.657-685, 1998.
DOI : 10.1016/S0997-7538(99)80027-8

URL : https://hal.archives-ouvertes.fr/hal-00765806

S. Han and B. Feeny, Enhanced Proper Orthogonal Decomposition for the Modal Analysis of Homogeneous Structures, Journal of Vibration and Control, vol.8, issue.1, pp.19-40, 2002.
DOI : 10.1177/1077546302008001518

M. Amabili, A. Sarkar, and M. Paidoussis, Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method, Journal of Fluids and Structures, vol.18, issue.2, pp.227-250, 2003.
DOI : 10.1016/j.jfluidstructs.2003.06.002

G. Kerschen, J. Golinval, A. Vakakis, and L. Bergman, The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview, Nonlinear Dynamics, vol.16, issue.417???441, pp.147-169, 2005.
DOI : 10.1007/s11071-005-2803-2

R. Sampaio and C. Soize, Remarks on the efficiency of POD for model reduction in non-linear dynamics of continuous elastic systems, International Journal for Numerical Methods in Engineering, vol.45, issue.3, pp.22-45, 2007.
DOI : 10.1002/nme.1991

URL : https://hal.archives-ouvertes.fr/hal-00686148

K. Willcox and J. Peraire, Balanced Model Reduction via the Proper Orthogonal Decomposition, AIAA Journal, vol.40, issue.11, pp.2323-2330, 2002.
DOI : 10.2514/2.1570

C. Prudhomme, D. Rovas, K. Veroy, L. Machiels, Y. Maday et al., Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002.
DOI : 10.1115/1.1448332

URL : https://hal.archives-ouvertes.fr/hal-00798326

P. Astrid, S. Weiland, K. Willcox, and T. Backx, Missing Point Estimation in Models Described by Proper Orthogonal Decomposition, IEEE Transactions on Automatic Control, vol.53, issue.10, pp.2237-2251, 2008.
DOI : 10.1109/TAC.2008.2006102

P. Ciarlet, Mathematical Elasticity: Threedimensional elasticity, 1993.

Y. Fung and P. Tong, Classical and Computational Solid Mechanics, World Scientific, 2001.

B. Coleman and W. Noll, Foundations of linear viscoelasticity):239249. [84] Desceliers C, Soize C. Nonlinear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization, Review of Modern Physics International Journal of Non-linear Mechanics, vol.33, issue.393, pp.343-368, 1961.

O. Zienkiewicz and R. Taylor, The Finite Element Method for Solid and Structural Mechanics, 2005.

J. Bonet and R. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, 2008.
DOI : 10.1017/CBO9780511755446

P. Wriggers, Nonlinear Finite Element Methods, 2010.

D. Borst, R. Crisfield, M. Remmers, J. Verhoosel, and C. , Nonlinear Finite Element Analysis of Solids and Structures

T. Belytschko, W. Liu, B. Moran, and K. Elkhodary, Nonlinear Finite Elements for Continua and Structures

M. Mignolet, A. Przekop, S. Rizzi, and S. Spottswood, A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures, Journal of Sound and Vibration, vol.332, issue.10, pp.2437-2460, 2013.
DOI : 10.1016/j.jsv.2012.10.017

E. Van-brummelen, Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction, Journal of Applied Mechanics, vol.76, issue.2, pp.21206-21207, 2009.
DOI : 10.1115/1.3059565

E. Van-brummelen, Partitioned iterative solution methods for fluid-structure interaction, International Journal for Numerical Methods in Fluids, vol.193, issue.2, p.327, 2011.
DOI : 10.1002/fld.2465

E. Capiez-lernout, C. Soize, and M. Mignolet, Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.271, issue.1, pp.210-230, 2014.
DOI : 10.1016/j.cma.2013.12.011

URL : https://hal.archives-ouvertes.fr/hal-00922708

E. Capiez-lernout, C. Soize, and M. Mbaye, Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity, Journal of Sound and Vibration, vol.356, pp.124-143, 2015.
DOI : 10.1016/j.jsv.2015.07.006

URL : https://hal.archives-ouvertes.fr/hal-01183415

R. Perez, X. Wang, and M. Mignolet, Nonlinear Reduced-Order Models for Thermoelastodynamic Response of Isotropic and Functionally Graded Panels, AIAA Journal, vol.49, issue.3, pp.630-641, 2011.
DOI : 10.2514/1.J050684

R. Murthy, X. Wang, R. Perez, M. Mignolet, and L. Richter, Uncertainty-based experimental validation of nonlinear reduced order models, Journal of Sound and Vibration, vol.331, issue.5, pp.1097-1114, 2012.
DOI : 10.1016/j.jsv.2011.10.022