E. Albano and W. Et-rodden, A doublet lattice method for calculating lift distributions on oscillating surfaces in subsonic flows, 6th Aerospace Sciences Meeting, pp.279-285, 1969.
DOI : 10.2514/6.1968-73

L. Arnold, Stochastic differential equations: Theory and applications, 1974.

L. Arnold, A Formula Connecting Sample and Moment Stability of Linear Stochastic Systems, SIAM Journal on Applied Mathematics, vol.44, issue.4, pp.793-802, 1984.
DOI : 10.1137/0144057

L. Arnold, Lyapunov exponents of nonlinear differential stochastic systems. Dans Nonlinear stochastic dynamic engineering systems, Ziegler et G. Schueller, IUTAM Symposium Innsbruck/Igls, Austria, pp.181-201

L. Arnold, Random dynamical systems, 1998.

L. Arnold, S. Par, R. N. Narayanan, and . Iyengar, Recent Progress in Stochastic Bifurcation Theory, IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics edité, pp.15-27, 1999.
DOI : 10.1007/978-94-010-0886-0_2

L. Arnold, G. Bleckert, and K. Schenk-hoppé, The Stochastic Brusselator: Parametric Noise Destroys Hoft Bifurcation, Stochastic Dynamics, edité par H. Crauel et M. Gundlach, pp.71-90, 1999.
DOI : 10.1007/0-387-22655-9_4

L. Arnold, P. Et-boxler, H. Arnold, J. Crauel, and . Eckmann, Additive noise turns a hyperbolic fixed point into a stationary solution, Lyapunov exponents. Proceedings, pp.159-164, 1990.
DOI : 10.1007/BF00955515

L. Arnold and X. Et-kedai, Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point, Random and Computational Dynamics, vol.2, issue.2, pp.165-182, 1994.

L. Arnold, W. Kliemann, E. Et-oeljeklaus, V. Arnold, and . Wihstutz, Lyapunov exponents of linear stochastic systems, Lecture Notes in Mathematics, vol.12, pp.85-159, 1984.
DOI : 10.1016/0022-0396(72)90007-1

L. Arnold, E. Oeljeklaus, and E. Et-pardoux, Almost sure and moment stability for linear ito equations, Lecture Notes in Mathematics, vol.21, pp.85-159, 1984.
DOI : 10.1137/0321020

L. Arnold, N. Sri-namachchivaya, and K. R. Schenk-hoppé, TOWARD AN UNDERSTANDING OF STOCHASTIC HOPF BIFURCATION, International Journal of Bifurcation and Chaos, vol.06, issue.11, pp.1947-1975, 1996.
DOI : 10.1142/S0218127496001272

J. Bae, D. Inman, and I. Et-lee, Effects of structural nonlinearity on subsonic aeroelastic characteristics of an aircraft wing with control surface, Journal of Fluids and Structures, vol.19, issue.6, pp.747-763, 2004.
DOI : 10.1016/j.jfluidstructs.2004.04.005

P. Ballard, The Dynamics of Discrete Mechanical Systems with Perfect Unilateral Constraints, Archive for Rational Mechanics and Analysis, vol.154, issue.3, pp.199-274, 2000.
DOI : 10.1007/s002050000105

URL : https://hal.archives-ouvertes.fr/hal-00111308

K. Bathe and P. Et-bouzinov, On the constraint function method for contact problems, Computers & Structures, vol.64, issue.5-6, pp.1069-1085, 1997.
DOI : 10.1016/S0045-7949(97)00036-9

K. Bathe and E. Et-wilson, Numerical methods in finite element analysis, 1976.

O. A. Bauchau, J. Rodriguez, and C. L. Et-bottasso, Modeling of unilateral contact conditions with application to aerospace systems involving backlash, freeplay and friction, Mechanics Research Communications, vol.28, issue.5, pp.571-599, 2001.
DOI : 10.1016/S0093-6413(01)00210-5

D. Berggren, Investigation of limit cycle oscillations for a wing section with nonlinear stiffness, Aerospace Science and Technology, vol.8, issue.1, pp.27-34, 2004.
DOI : 10.1016/j.ast.2003.08.006

P. Bernard and C. Et-bonnemoy, An algorithm for spectral factorization using random search techniques, Probabilistic Engineering Mechanics, pp.66-73, 1989.
DOI : 10.1016/0266-8920(89)90011-8

P. Bernard, M. Fogli, P. Bressolette, and M. Et-lemaire, Un algorithme de simulation stochastique par markovianisation approchée, applicationàapplicationà la mécanique aléatoire, Journal de Mécanique Théorique et Appliquée, vol.3, issue.6, pp.905-950, 1984.

R. Bhattacharya, On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.5, issue.2, pp.185-201, 1982.
DOI : 10.1007/BF00531822

P. Boxler, A stochastic version of center manifold theory. Probability Theory and Realted Fields, pp.509-545, 1989.

P. Boxler, Lyapunov exponents indicate stability and detect stochastic bifurcations . Dans Probabilistic methods in applied physics, Lecture Notes in Physics, pp.97-119, 1995.

P. Boxler, Stochastic center as a tool in a stochastic bifurcation theory. Dans Probabilistic methods in applied physics, Lecture Notes in Physics, pp.149-166, 1995.

E. Breitbach, Effects of structural nonlinearities on aircraft vibration and flutter, Rap. tech. NATO AGARD, vol.665, 1978.

B. Brogliato, Nonsmooth Mechanics. Models, Dynamics and Control, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01236953

B. Brogliato, Absolute stability and the Lagrange???Dirichlet theorem with monotone multivalued mappings, Systems & Control Letters, vol.51, issue.5, pp.343-353, 2004.
DOI : 10.1016/j.sysconle.2003.09.007

URL : https://hal.archives-ouvertes.fr/inria-00071792

C. Bucher and Y. Et-lin, Effect of spanwise correlation of turbulence field on the motion stability of long-span bridges, Journal of Fluids and Structures, vol.2, issue.5, pp.437-451, 1988.
DOI : 10.1016/S0889-9746(88)90159-4

C. Bucher and Y. Et-lin, Stochastic Stability of Bridges Considering Coupled Modes, Journal of Engineering Mechanics, vol.114, issue.12, pp.2055-2071, 1988.
DOI : 10.1061/(ASCE)0733-9399(1988)114:12(2055)

M. Castanier and C. Et-pierre, Lyapunov exponents and localization phenomena in multi-coupled nearly periodic systems, Journal of Sound and Vibration, vol.183, issue.3, pp.493-515, 1995.
DOI : 10.1006/jsvi.1995.0267

T. Cowan, A. Arena, and K. Et-gupta, Accelerating Computational Fluid Dynamics Based Aeroelastic Predictions Using System Identification, Journal of Aircraft, vol.38, issue.1, pp.81-87, 2001.
DOI : 10.2514/2.2737

R. Craig and M. Et-bampton, Coupling of substructures for dynamic analyses, AIAA Journal, vol.6, issue.7, pp.1313-1319, 1968.

R. Dautry and J. Et-lions, Mathematical analysis and numerical methods for science and engineering, 1992.

M. Dellnitz and A. Et-hohmann, A subdivision algorithm for the computation of unstable manifolds and global attractors, Numerische Mathematik, vol.75, issue.3, pp.293-317, 1997.
DOI : 10.1007/s002110050240

Z. Dimitrijevic, Détermination des bifurcations de Hopf et des cycles limites d'une structure non linéaire soumisè a unécoulementunécoulement transsonique d'un fluide parfait, Thèse de doctorat, 2000.

Z. Dimitrijevic, G. Mortchelewicz, and F. Et-poirion, Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow, Aerospace Science and Technology, vol.4, issue.2, pp.125-133, 2000.
DOI : 10.1016/S1270-9638(00)00127-9

E. Doedel, Lecture notes on numerical analysis of bifurcation problems. pub/doedel/doc/hamburg.ps, 1997.

E. Dowell, J. Edwards, T. Et-strganac, and . Nonlinear-aeroelasticity, Nonlinear Aeroelasticity, Journal of Aircraft, vol.40, issue.5, pp.857-873, 2003.
DOI : 10.2514/2.6876

E. Dowell, J. Thomas, and K. Hall, Transonic limit cycle oscillation analysis using reduced order aerodynamic models, Journal of Fluids and Structures, vol.19, issue.1, pp.17-27, 2004.
DOI : 10.1016/j.jfluidstructs.2003.07.018

M. Doyle, N. Sri-namachchivaya, and H. Van-roessel, Asymptotic stability of structural systems based on Lyapunov exponents and moment Lyapunov exponents, International Journal of Non-Linear Mechanics, vol.32, issue.4, pp.681-692, 1997.
DOI : 10.1016/S0020-7462(96)00093-5

M. Duflo, Algorithmes stochastiques, 1996.

Y. Fung, An introduction to the theory of aeroelasticity, 1955.

H. Furstenberg, Noncommuting random products, Transactions of the American Mathematical Society, vol.108, issue.3, pp.377-428, 1963.
DOI : 10.1090/S0002-9947-1963-0163345-0

P. Germain, Cours de mécanique des milieux continus, 1973.

J. Grisval, J. Meurzec, and F. Et-poirion, Numerical method for the response of an aircraft to the atmospheric turbulence. Application to the Nord 260 airplane, Proceedings of the European Forum on Aeroelasticity and Structural Dynamics, pp.351-357, 1989.

A. Grorud and D. Et-talay, Approximation of Lyapunov Exponents of Nonlinear Stochastic Differential Equations, SIAM Journal on Applied Mathematics, vol.56, issue.2, pp.627-650, 1996.
DOI : 10.1137/S0036139992227710

J. Guckenheimer and P. Et-holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, 1983.

W. Horsthemke and R. Et-lefever, Noise-induced transitions, 1984.
DOI : 10.1017/CBO9780511897825.010

J. C. Houbolt, Atmospheric Turbulence, AIAA Journal, vol.11, issue.4, pp.421-437, 1973.
DOI : 10.2514/3.50485

Y. Hurmuzlu, An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces, Journal of Applied Mechanics, vol.65, issue.4, pp.952-962, 1998.
DOI : 10.1115/1.2791939

M. Jean, The non-smooth contact dynamics method, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.235-257, 1999.
DOI : 10.1016/S0045-7825(98)00383-1

URL : https://hal.archives-ouvertes.fr/hal-01390459

M. Karpel, Design for Active Flutter Suppression and Gust Alleviation Using State-Space Aeroelastic Modeling, Journal of Aircraft, vol.19, issue.3, pp.221-227, 1982.
DOI : 10.2514/3.57379

H. Keller and G. Et-ochs, Numerical Approximation of Random Attractors, Stochastic Dynamics, edité par H. Crauel et M. Gundlach, pp.93-114
DOI : 10.1007/0-387-22655-9_5

R. Khasminskii, Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems, Theory of Probability & Its Applications, vol.12, issue.1, pp.144-147, 1967.
DOI : 10.1137/1112019

W. Kliemann and F. Et-colonius, Ergodic theory of stochastic flows. Dans Diffusion processes and related problems in analysis, volume II: Stochastic flows, pp.203-239, 1992.

P. E. Kloeden and E. Et-platen, Numerical solution of stochastic differential equations, 1992.

K. Kousen and O. Et-bendiksen, Limit cycle phenomena in computational transonic aeroelasticity, Journal of Aircraft, vol.31, issue.6, pp.1257-1263, 1994.
DOI : 10.2514/3.46644

P. Kree and C. Et-soize, Mathematics of Random Phenomena, 1986.
DOI : 10.1007/978-94-009-4770-2

URL : https://hal.archives-ouvertes.fr/hal-00770408

M. Kunze and T. Et-küpper, Nonsmooth dynamical systems: An overview. Dans Ergodic Theory, Analysis, and Efficient Simulation of Dynamical systems, edité par B. Fiedler, pp.431-452, 2001.

M. Kunze and M. Et-monteiro-marques, An introduction to Moreau's sweeping process. Dans Impacts in Mechanical Systems, Analysis and Modelling, pp.1-60, 2000.

B. Lee, S. Price, and Y. Et-wong, Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos, Progress in Aerospace Sciences, pp.205-334, 1999.
DOI : 10.1016/S0376-0421(98)00015-3

Q. Li and Y. Et-lin, New Stochastic Theory for Bridge Stability in Turbulent Flow. II, Journal of Engineering Mechanics, vol.121, issue.1, pp.102-116, 1995.
DOI : 10.1061/(ASCE)0733-9399(1995)121:1(102)

Y. Lin and S. Et-ariaratnam, Stability of Bridge Motion in Turbulent Winds, Journal of Structural Mechanics, vol.3, issue.2, pp.1-15, 1988.
DOI : 10.1080/03601218008907350

L. Liu, Y. Wong, and B. Et-lee, APPLICATION OF THE CENTRE MANIFOLD THEORY IN NON-LINEAR AEROELASTICITY, Journal of Sound and Vibration, vol.234, issue.4, pp.641-659, 2000.
DOI : 10.1006/jsvi.1999.2895

D. Lucia and P. B. Silva, Reduced-order modeling: new approaches for computational physics, Progress in Aerospace Sciences, vol.40, issue.1-2, pp.51-117, 2004.
DOI : 10.1016/j.paerosci.2003.12.001

M. Mabrouk, A unified variational model for the dynamics of perfect unilateral constraints, European Journal of Mechanics - A/Solids, vol.17, issue.5, pp.819-842, 1998.
DOI : 10.1016/S0997-7538(98)80007-7

M. Marques and M. , Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and dry friction, Birkhäuser, 1993.

J. Moreau, Liaisons unilatérales sans frottement et chocs inélastiques, C. R. Acad. Sc. Paris, Série II, vol.296, pp.1473-1476, 1983.

J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, Nonsmooth mechanics and Applications Moreau et P. Panagiotopoulus , tm. 302 de CISM Courses and Lectures, pp.1-82, 1988.
DOI : 10.1007/978-3-7091-2624-0_1

J. Moreau, Numerical aspects of the sweeping process, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.329-349, 1999.
DOI : 10.1016/S0045-7825(98)00387-9

URL : https://hal.archives-ouvertes.fr/hal-01349847

G. Mortchelewicz, Application of the linearized Euler equations to flutter, 1997.

G. Mortchelewicz and L. Et-daudois, Limit cycle analysis of a structure in an inviscid compressible flow in presence of freeplay nonlinearities, 42nd Israel Annual Conference on Aerospace Sciences, 2002.

T. Most, C. Bucher, and Y. Et-schorling, Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading, Journal of Sound and Vibration, vol.276, issue.1-2, pp.381-400, 2004.
DOI : 10.1016/j.jsv.2003.07.038

V. Oseledets, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Mathematical Society, vol.19, pp.197-231, 1968.

L. Paoli and M. Et-schatzmann, Dynamics of an impacting bar, Proceedings of ECCM'99, 1999.

L. Paoli and M. Et-schatzmann, Penalty approximation for dynamical systems submitted to multiple non-smooth constraints, Multibody System Dynamics, vol.8, issue.3, pp.345-364, 2002.
DOI : 10.1023/A:1020977815807

E. Pardoux and D. Et-talay, Stability of linear differential systems with parametric excitation. Dans Nonlinear stochastic dynamic engineering systems, Ziegler et G. Schueller, IUTAM Symposium Innsbruck/Igls, Austria, pp.153-168, 1988.

D. Peters, S. Karunamoorthy, W. Cao, and C. Et-he, Finite state induced flow models. I - Two-dimensional thin airfoil, Journal of Aircraft, vol.32, issue.2, pp.313-333, 1995.
DOI : 10.2514/3.46718

O. Pironneau and C. Et-bardos, Petites perturbations etéquationsetéquations d'Euler pour l'aéroélasticité, Mathematical Modelling And Numerical Analysis, vol.28, issue.4, pp.463-407, 1994.

D. Poirel and S. Et-price, Post-Instability Behavior of a Structurally Nonlinear Airfoil in Longitudinal Turbulence, Journal of Aircraft, vol.34, issue.5, pp.619-626, 1997.
DOI : 10.2514/2.2238

D. Poirel and S. Et-price, Structurally Nonlinear Fluttering Airfoil in Turbulent Flow, AIAA Journal, vol.39, issue.10, pp.1960-1968, 2001.
DOI : 10.2514/2.1186

D. Poirel and S. Et-price, Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow, Probabilistic Engineering Mechanics, vol.18, issue.2, pp.185-202, 2003.
DOI : 10.1016/S0266-8920(03)00013-4

F. Poirion, Modélisation et prise en compte des incertitudes dans les modèles numériques de prévision des instabilités aéroélastiques, La Recherche Aérospatiale, vol.1, issue.6, pp.31-41, 1992.

F. Poirion, Modélisation temporelle des systèmes aéroélastiques Applicationà Applicationà l'´ etude des rétards, La Recherche Aérospatiale, issue.2, pp.103-114, 1995.

F. Poirion, On some stochastic methods applied to aeroservoelasticity, Aerospace Science and Technology, vol.4, issue.3, pp.201-214, 2000.
DOI : 10.1016/S1270-9638(00)00118-8

F. Poirion and J. Et-angelini, Vibrations aléatoires avec contraintes: Modélisation et résolution numérique dans le cas d'une gouverne, La Recherche Aérospatiale, issue.6, pp.385-394, 1985.

F. Poirion and I. Et-zentner, Nonsmooth dynamics of aeroelastic systems featuring a freeplay nonlinearity, International Journal of Non-Linear Mechanics, 2005.

S. Price, H. Alighanbari, and B. Et-lee, The Aeroelastic Response of a Two-Dimensional Airfoil with Bilinear and Cubic Structural Nonlinearities, Journal of Fluids and Structures, vol.9, issue.2, pp.175-193, 1995.
DOI : 10.1006/jfls.1995.1009

K. Roger, Airplane math modeling methods for active control design. structural aspects of active controls, Rap. tech. CP, vol.228, p.AGARD, 1977.

R. Roos and R. Et-zwaan, Calculation of instationary pressure distributions and generalized aerodynamic forces with the doublet-lattice method. Rap. tech, 1972.

D. Ruelle, Chaotic evolution and strange attractors: the statistical analysis of time series for deterministic nonlinear systems, 1989.
DOI : 10.1017/CBO9780511608773

R. Scanlan and J. Et-tomko, Airfoil and bridge deck flutter derivatives, Journal of the Engineering Mechanics Division, vol.97, issue.EM6, pp.1717-1737, 1971.

M. Schatzmann, A class of nonlinear differential equations of second order in time, Nonlinear Analysis: Theory, Methods & Applications, vol.2, issue.3, pp.355-373, 1998.
DOI : 10.1016/0362-546X(78)90022-6

K. R. Schenk-hoppé, Bifurcation scenarios of the noisy duffing-van der pol oscillator, Nonlinear Dynamics, vol.58, issue.3, pp.255-274, 1996.
DOI : 10.1007/BF00120720

K. R. Schenk-hoppé, Stochastic Hopf bifurcation: An example, International Journal of Non-Linear Mechanics, vol.31, issue.5, pp.685-692, 1996.
DOI : 10.1016/0020-7462(96)00030-3

R. Seifried, W. Schiehlen, and P. Et-eberhardt, Numerical and experimental evaluation of the coefficient of restitution for repeated impacts, International Journal of Impact Engineering, vol.32, issue.1-4, 2005.
DOI : 10.1016/j.ijimpeng.2005.01.001

W. Silva, Application of nonlinear systems theory to unsteady transonic aerodynamic responses, J. Aircraft, vol.30, issue.5, pp.660-668, 1993.

S. Namachcchivaya, N. Roessel, H. V. Et-doyle, and M. , Moment Lyapunov Exponent for Two Coupled Oscillators Driven by Real Noise, SIAM Journal on Applied Mathematics, vol.56, issue.5, pp.1400-1423, 1996.
DOI : 10.1137/S003613999528138X

S. Namachchivaya, N. Et-vedula, and L. , Stabilization of linear systems by noise: Application to flow induced oscillations, Dynamics and Stability of Systems, vol.22, issue.2, pp.185-208, 2000.
DOI : 10.1137/S003613999528138X

D. Talay, Approximation of Upper Lyapunov Exponents of Bilinear Stochastic Differential Systems, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.1141-1164, 1991.
DOI : 10.1137/0728061

URL : https://hal.archives-ouvertes.fr/inria-00075594

D. Tang, E. Dowell, and L. Et-virgin, LIMIT CYCLE BEHAVIOR OF AN AIRFOIL WITH A CONTROL SURFACE, Journal of Fluids and Structures, vol.12, issue.7, pp.839-858, 1998.
DOI : 10.1006/jfls.1998.0174

T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter, Rap. tech. NACA report, vol.496, 1934.

B. Van-der-wall and J. Et-leishmann, On the Influence of Time-Varying Flow Velocity on Unsteady Aerodynamics, Journal of the American Helicopter Society, vol.39, issue.4, pp.25-36, 1994.
DOI : 10.4050/JAHS.39.25

M. Vidyasagar, Nonlinear systems analysis, 1978.

P. Viguier, Wind tunnel test of a non-linear flutter model, Proceedings of IFASD'03, 2003.

H. Wagner, ¨ Uber die Entstehung des dynamischen Auftriebes von Tragflügeln, Math. Mech, 1925.

T. Wanner, Linearization of Random Dynamical Systems, pp.203-269, 1995.
DOI : 10.1007/978-3-642-61215-2_4

A. Wolf, J. Swift, H. Swinney, and A. Vastano, Determining Lyapunov exponents from a time series, Physica D: Nonlinear Phenomena, vol.16, issue.3, pp.285-317, 1985.
DOI : 10.1016/0167-2789(85)90011-9

W. Xie, Moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation, Journal of Sound and Vibration, vol.263, issue.3, pp.593-616, 2003.
DOI : 10.1016/S0022-460X(02)01068-4

W. Xie and S. Et-ariaratnam, VIBRATION MODE LOCALIZATION IN DISORDERED CYCLIC STRUCTURES, I: SINGLE SUBSTRUCTURE MODE, Journal of Sound and Vibration, vol.189, issue.5, pp.625-660, 1996.
DOI : 10.1006/jsvi.1996.0040

E. Zeeman, Stability of dynamical systems, Nonlinearity, vol.1, issue.1, pp.115-155, 1988.
DOI : 10.1088/0951-7715/1/1/005

I. Zentner, Modélisation de la turbulence atmosphérique: Application auxéoauxéoliennes, ONERA, 2002.

I. Zentner and F. Et-poirion, Stochastic stability of fluid-structure coupled systems with multiplicative and additive noise: Application to airfoil flutter, Proceedings of the Fourth Conference on Engineering Computational Technology, pp.CD-ROM, 2004.

I. Zentner and F. Et-poirion, Flutter stability of aircraft subjected to random fluctuations of the flow velocity, Proceedings of IFASD'05, 2005.

I. Zentner and F. Et-poirion, Stability of aircraft in turbulent flow based on the theory of random dynamical systems, Proceedings of Icossar'05, 2005.

O. Zienkiewicz and R. Et-taylor, The finite element method, 1989.