E. L. Bibliographieallgower-et-georg-]-allgower and K. Tgeorg, Introduction to Numerical Continuation Methods.S p r i n g e r -V e r l a g, 2003.

. Benfield, . Hruda, W. A. Benfield, and R. F. Thruda, Vibration Analysis of Structures by Component Mode Substitution, AIAA Journal, vol.9, issue.7, pp.1255-1256, 1971.
DOI : 10.2514/3.49936

. Blair, Harmonic balance and continuation techniques in the dynamicanalysisofduffing's equation, Journal of Sound and Vibration, vol.12, issue.1 5, pp.0-2

A. Bobillot, Méthodes de réduction pour le recalage Application au cas d'Ariane 5, 2002.

C. , G. Cameron, T. M. Etgriffin, and J. H. , A nal te rn ating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems, Journal of Applied Mechanics, vol.6, issue.1, pp.1-4, 1989.

. Cardona, 9 8 ) . F a s t fourier nonlinear vibration analysis, Computational Mechanics, vol.1, issue.9

D. Charleux, Etude de la friction en pied d'aube sur la dynamique des roues aubagées, 2006.

C. Et-menq-]-chen, J. J. Tmenq, and C. H. , 0 0 1 ) . P e r i o d i cr e s p o n s eo f blades having three-dimensional nonlinear shroud constraints, Journal of Engineering for Gas Turbines and Power, vol.1, issue.2 4, pp.2-3, 2001.

. Cheung, A p p l i c a tion of the incremental harmonic balance method to cubic non-linearity systems, Journal of Sound and Vibration, vol.11, issue.0 2, pp.0-2

D. W. Childs, Turbomachinery rotordynamics -Phenomena, modeling and analysis, 1993.

N. Choi, Y. S. Choi, and S. T. Tnoah, 9 8 7 ) . N o n l i n e a rs t e a d ys t a t e response of a rotor-support system, Journal of Vibration Accoustics, Stress and Reliability in Design, issue.1, 1987.

. Cochelin, B. Vergez-]-cochelin, and C. Tvergez, 0 0 9 ) Ah i g ho r d e rp u rely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, vol.3, issue.2, pp.2-4, 2009.

T. Cooley, J. W. Cooley, and J. W. Ttukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

N. Coudeyras, Analyse non-linéaire des instabilités multiples aux interfaces frottantes : application au crissement de frein.T h è s e de doctorat, 2009.

. Coudeyras, A new treatment for predicting the self-excited vibrations ofnonlinearsystemswith frictional interfaces : The constrained harmonic balance method, with application to disc brake squeal, Journal of Sound and Vibration, vol.3, pp.1-9

C. Et-bampton-]-craig, R. R. Tbampton, and M. C. , C o u p l i n g of structures for dynamic analyses, AIAA Journal, vol.6, issue.7, pp.1-3, 1968.

C. , C. Craig, R. R. Tchang, and C. , F r e e -i n t e r f a c em e thods of substructures coupling for dynamic analysis, AIAA Journal, issue.11, pp.141633-141634, 1976.

D. Demailly, Étude du comportement non-linéaire dans le domaine fréquentiel. Application à la dynamique rotor, 2003.

D. Et-prince-]-dormand, J. R. Tprince, and P. J. , Af a m i l yo f embedded runge-kutta formulae, Journal of Computational and Applied Mathematics, vol.6, issue.1, pp.1-9, 1980.

F. Ehrich, Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics, Journal of Vibration and Acoustics, vol.114, issue.1, pp.93-100, 1992.
DOI : 10.1115/1.2930240

F. F. Ehrich, Handbook of Rotordynamics.K r i e g e rP u b l i shing Co, 1999.

D. J. Ewins, Modal Testing : Theory, Practice and Application .R e s e a r c hS t u d i e sP r e s s, 2000.
DOI : 10.1115/1.3269294

R. Fletcher, Practical methods of optimization, second edition.J o h nW i l e y&S o n s, 2000.

V. Fridrici, Fretting d'un al liage de titane revêtu et lubrifié : application au contact aube/disque, 2002.

R. Ganesan, Nonlinearvibrationsandstabilityofarotor- bearing system with nonsymmetric clearances, Journal of Engineering for Gas Turbines and Power, vol.1, issue.9 2, pp.4-5, 1997.
DOI : 10.1115/1.2815591

G. Genta, Whirling of unsymmetrical rotors: A finite element approach based on complex co-ordinates, Journal of Sound and Vibration, vol.124, issue.1, pp.27-53, 1988.
DOI : 10.1016/S0022-460X(88)81404-4

G. Et-rixen-]-géradin, M. Trixen, and D. , Théorie des Vibrations , Application à la dynamique des structures.M a s s o n, 1993.

. Groll, . Ewins, G. V. Groll, and D. Tewins, 0 0 1 ) . T h eh a r m o n i cb a l a n c e method with arc-length continuation in rotor/stator contact problems, Journal of Sound and Vibration, vol.2, issue.2 2, pp.4-5, 2001.

. Guskov, M u l t i dimensional harmonic balance applied to rotor dynamics, Mechanics Research Communications, issue.8, pp.5-5

. Hall, Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines
DOI : 10.1007/1-4020-4605-7

. Hashish, . Sankar, E. Hashish, and T. S. Tsankar, 9 8 4 ) . F i n i t ee l e m e n t and modal analyses of rotor-bearing systems under stochastic loading conditions, Journal of Vibration Acoustics Stress and Reliability in Design, vol.1, issue.1 1, pp.0-6, 1984.

R. Henry, C a l c u ld e sf r é q u e n c e se tm o d e sd e ss t r u c t u r e s répétitives circulaires, Journal de Mécanique Appliquée, vol.4, issue.1, pp.6-7, 1980.

W. C. Hurty, ( 1 9 6 5 ) D y n a m i ca n a l y s i so fs t r u c t u r a ls y s t e m su s i n g component modes, AIAA Journal, vol.3, issue.4, pp.6-7, 1965.

. Ji, . Zu, Z. Ji, and J. Tzu, M e t h o do fm u l t i p l es c a l e sf o rv i b r a t i o n analysis of rotor shaft systems with non-linear bearing pedestal model, Journal of Sound and Vibration, vol.12, issue.2, pp.1-8, 1998.

. Khader, . Loewy, N. Khader, and R. G. Tloewy, 9 9 0 ) S h a f tfl e x i b i l i t y effects on the forced response of a bladed-disk assembly, Journal of Sound and Vibration, vol.11, issue.9 3, pp.4-6, 1990.

. Kim, Periodicresponseofmulti- disk rotors with bearing clearances, Journal of Sound and Vibration, vol.11, issue.3, pp.4-4, 1991.
DOI : 10.1016/0022-460x(91)90558-2

D. Ku, 9 8 ) . F i n i t ee l e m e n ta n a l y s i so fw h i r ls p e e d sf o rr otorbearing systems with internal damping, Mechanical Systems and Signal Processing, p.5, 1998.

L. Et-ferraris-]-lalanne, M. Tferraris, and G. , Rotordynamics Prediction in Engineering, 1998.

. Lau, 8 3 ) . I n c r e m e n t a l harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems, Journal of Applied Mechanics, vol.1, issue.9 0 4, pp.8-15

L. Et-thouverez-]-laxalde, D. Tthouverez, and F. , C o m p l e x non-linear modal analysis for mechanical systems : Application to turbomachinery bladings with friction interfaces, Journal of Sound and Vibration, vol.3, pp.2-2, 2009.

. Laxalde, Dynamical analysis of multi-stage cyclic structures, Mechanics Research Communications, vol.34, issue.4, pp.3-7
DOI : 10.1016/j.mechrescom.2007.02.004

URL : https://hal.archives-ouvertes.fr/hal-00227538

L. , T. Lazarus, A. Etthomas, and O. , Aharmonic-based method for computing the stability of periodic solutions of dynamical systems, Comptes Rendus Mécanique, vol.3, issue.9, pp.3-8, 2010.

. Lee, . Lee, Y. Lee, and C. Tlee, M o d e l l i n ga n dv i b r a t i o na n a lysis of misaligned rotor-ball bearing systems, Journal of Sound and Vibration, vol.1, issue.2241, pp.17-32, 1999.

. Legrand, 1 0 ) . S t r u c t u ral modal interaction of a four degree-of-freedom bladed disk and casing model, Journal of Computational and Nonlinear Dynamics, vol.25, issue.0 4

N. Lesaffre, Stabilité et Analyse Linéaire du Contact Rotor-Stator, 2007.

. Lesaffre, S t a bility analysis of rotating beams rubbing on an elastic circular structure, Journal of Sound and Vibration, vol.2, pp.9-9

. Liew, T r a n s i e n tr o t o r d y namic modeling of rolling element bearing systems, Journal of Engineering for Gas Turbines and Power, vol.1, issue.2 4, pp.2-4

R. H. Macneal, Ah y b r i dm e t h o do fc o m p o n e n tm o d e synthesis, Computers & Structures, vol.1, issue.4, pp.5-8, 1971.

D. R. Merkin, Introduction to the theory of stability, 1997.
DOI : 10.1007/978-1-4612-4046-4

. Millecamps, ) . I n fl u e n c eo ft h e r m a le ffects during blade-casing contact experiments, ASME Conference Proceedings

. Murthy, E fficient modeling of fretting of blade/disk contacts including load history effects, Journal of Tribology, vol.1, issue.1, pp.2-6, 2004.

. Nacivet, A dynamic lagrangian frequency-time method for the vibration of dryfriction-damped systems, Journal of Sound and Vibration, vol.2, issue.1, pp.6-11, 2003.

. Narayanan, . Sekar, S. Narayanan, and P. Tsekar, 9 9 8 )Af r e q u e n c yd o main based numeric-analytical method for non-linear dynamical systems, Journal of Sound and Vibration, vol.12, issue.3, pp.1-1, 1998.

N. Et-balachandran, A. H. Nayfeh, and B. Etbalachandran, Ap- plied Nonlinear Dynamics.W i l e yS e r i e si nN o n l i n e a rS c i e n c e, 1995.

F. C. Nelson, Ar e v i e wo ft h eo r i g i n sa n dc u r r e n ts t a t u so f rotor dynamics, Sixth International Conference on Rotor Dynamics, 2002.

N. Nelson, H. D. Tmcvaugh, and J. M. , T h ed y n amics of rotor-bearing systems using finite elements, Journal of Engineering for Industry, vol.8, issue.2, pp.5-9, 1976.

Ö. Et-Özkan-]-Özgüven, H. N. Tözkan, and Z. L. , W h i r ls p e e d s and unbalance response of multibearing rotors using finite elements, Journal of Vibration Acoustics Stress and Reliability in Design, vol.1, issue.1, pp.0-6, 1984.

E. P. Petrov, Amethodforuseofcyclicsymmetryproper- ties in analysis of nonlinear multiharmonic vibrations of bladed disks, Journal of Turbomachinery, vol.1, issue.6 1, pp.1-7, 2004.

E. P. Petrov and D. J. Tewins, A n a l y t i c a lf o r mulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed discs, ASME Conference Proceedings, 2002.

C. Pierre, M o d el o c a l i z a t i o na n de i g e n v a l u el o c iv e e r i n g phenomena in disordered structures, Journal of Sound and Vibration, issue.3, pp.126485-502, 1988.

P. Poudou, O. Poudou, and C. Tpierre, ) . é t u d ed el ar é p o n s e forcée élastique d'une roue aubagée amortie par frotteurs det y p ec o i n:a n a l y s e théorique et simulations numériques, 14 ème Colloque Vibration, p.17, 2004.

S. Saito, er e s p o n s eo fhorizontal jeffcott rotors supported by ball bearings with radial clearances, Journal of Vibration Accoustics, Stress and Reliability in Design, 1985.
DOI : 10.1115/1.3269282

L. Salles, 0 1 0 ) Étude de l'usure par fretting sous chargements dynamiques dans les interfaces frottantes Application auxp i e d sd ' a u b e sd et u r b o machines, 2010.

. Salles, Dynamic analysis of fretting-wear in friction contact interfaces, International Journal of Solids and Structures, vol.2, issue.1, 2011.

. Siewert, Wa l l a s c h e k Multiharmonic forced response analysis of a turbineb l a d i n gc o u p l e db y nonlinear contact forces, J.etRichter,C. Journal of Engineering for Gas Turbines and Power, issue.8, p.132082501, 2010.

S. Sinha, D y n a m i cc h a r a c t e r i s t i c so fafl e x i b l eb l a d e d -r o tor with coulomb damping due to tip-rub, Journal of Sound and Vibration, vol.2, issue.4, pp.7-10

S. K. Sinha, N o n -l i n e a rd y n a m i cr e s p o n s eo far o t a t i n gr a dial timoshenko beam with periodic pulse loading at the free-end, International Journal of Non-Linear Mechanics, issue.5, 2005.

N. Sundararajan, P. Sundararajan, and S. T. Tnoah, D y n a mics of forced nonlinear systems using shooting/arc-lengthcontinuationmethod? application to rotor systems, Journal of Vibration and Acoustics, vol.11, issue.9 1, pp.9-11, 1997.

. Szwedowicz, 0 0 8 ) . O nn o n l i n e a rf o r c e dv i b r a t i o no fs h r o u d e dt u r bine blades, Journal of Turbomachinery, issue.2

D. L. Thomas, Dynamics of rotationally periodic structures, International Journal for Numerical Methods in Engineering, vol.57, issue.1, pp.81-102, 1979.
DOI : 10.1002/nme.1620140107

. Tiwari, D y n a m i c response of an unbalanced rotor supported on ball bearings, Journal of Sound and Vibration, vol.2, issue.5, pp.3-8

. Tiwari, b ) . E ffect of radial internal clearance of a ball bearing on the dynamics ofabalancedhorizontal rotor, Journal of Sound and Vibration, vol.2, issue.5, pp.3-8
URL : https://hal.archives-ouvertes.fr/in2p3-00187053

S. Viana and C. Villa, Dynamique non-linéaire des rotors. Applications numériques et expérimentales à un rotor flexible.T h è s e de doctorat, 2005.

J. Wildheim, 1 9 8 1 ) E x c i t a t i o no fr o t a t i n gc i r c u m f e r e n t i a l l y periodic structures, Journal of Sound and Vibration, vol.7, issue.3, pp.5-8, 1981.

W. Et-ohayon-]-wildheim, R. Tohayon, and R. , T h é o r i ee tc a l cul statique et dynamique des structures à symétries cycliques, La Recherche aérospatiale, vol.4, pp.2-5, 1985.

S. J. Wildheim, Excitationofrotationallyperiodicstruc- tures, Journal of Applied Mechanics,4, vol.6, issue.4, pp.8-15, 1979.

L. Xie, G. Xie, and J. Y. Tlou, 9 6 ) A l t e r n a t i n gf r e q u e n c y / c o e fficient (afc) technique in the trigonometric collocation method, International Journal of Non-Linear Mechanics, vol.1, issue.1 4, pp.5-8, 1996.

. Zhao, S t a bility and bifurcation of unbalanced response of a squeeze film damped flexible rotor, Journal of Tribology, vol.11, issue.1 2, pp.1-6

. Zhao, S u b harmonic and quasi-periodic motions of an eccentric squeezefilmdamper-mounted rigid rotor, Journal of Vibration and Acoustics, vol.11, issue.3, pp.1-6, 1994.

N. Zorzi, E. S. Zorzi, and H. D. Tnelson, F i n i t ee l e m e n ts i mulation of rotor-bearing systems with internal damping, Journal of Engineering for Power, vol.9, issue.1, pp.9-16, 1977.

C. Diagramme-de, en haut) et réponse à balourd (en bas) du système axisymétrique en repère fixe, p.23

C. Diagramme-de, en haut) et réponse à balourd (en bas) du système axisymétrique en repère tournant, p.24

C. Diagramme-de, en haut) et réponse à balourd (en bas) du système à parties fixes dissymétriques en repère fixe, p.5

H. Diagramme-de-campbell-du-bi-la-synchrone, BP avec (?)l e sm od e sd ' e n s e m b l e ,( ?)l e sm od e sp u rd

R. , J. Dans-samcef, and .. , 116 IV.2 Cas-test de validation, IV.1 Définition des repères locaux tournants 118 IV.3 Secteur de référence du cas-test de validation . . . . . . . .......1 2, p.0

.. Réponse-linéaire-du-système-couplé-soumis-au-balourd-hp-y-tuhp, R é ponse du rotor BP en l'abscisse y FAN et (b) Réponse du rotor HP en l'abscisse, p.8