K. France and G. Rotex, Catalogue 3-GS-F-f-4

J. Argyris and H. P. Mlejnek, Texts on computational mechanics. Volume V Dynamics of structure, 1991.

G. Asch, Les capteurs en instrumentation industrielle. Dunod, fourth edition, 1996.

C. D. Bailey, Application of Hamilton's law of varying action, AIAA Journal, vol.13, issue.9, pp.1154-1157, 1975.
DOI : 10.2514/3.6966

C. D. Bailey, Comment on "When is Hamilton's Principle an Extremum Principle?", AIAA Journal, vol.13, issue.11, pp.1539-1540, 1975.
DOI : 10.2514/3.60568

C. D. Bailey, Comment on "Finite Elements for Initial Value Problems in Dynamics", AIAA Journal, vol.21, issue.1, pp.159-160, 1983.
DOI : 10.2514/3.60110

J. Barrault and S. Lasserre, Caractérisation de la résistancè a la fatigue en flexion ondulée de l'acier 35

J. Barrault and S. Lasserre, Limites de fatigue de l'acier 35 cd 4 en flexion rotative et en flexion plane

M. Baruch and R. Riff, Hamilton's principle, Hamilton's law - 6 to the n power correct formulations, AIAA Journal, vol.20, issue.5, pp.687-692, 1982.
DOI : 10.2514/3.7937

O. A. Bauchau and C. H. Hong, Nonlinear response and stability analysis of beams using finite elements in time, AIAA Journal, vol.26, issue.9, pp.1135-1142, 1988.
DOI : 10.2514/3.10021

P. V. Bayly, On the Spectral Signature of Weakly Bilinear Oscillators, Journal of Vibration and Acoustics, vol.118, issue.3, pp.352-361, 1996.
DOI : 10.1115/1.2888190

R. F. Beatty, Differentiating Rotor Response Due to Radial Rubbing, Journal of Vibration Acoustics Stress and Reliability in Design, vol.107, issue.2, pp.151-160, 1985.
DOI : 10.1115/1.3269238

K. B. Blair, C. M. Krousgrill, and T. N. Farris, HARMONIC BALANCE AND CONTINUATION TECHNIQUES IN THE DYNAMIC ANALYSIS OF DUFFING'S EQUATION, Journal of Sound and Vibration, vol.202, issue.5, pp.717-731, 1997.
DOI : 10.1006/jsvi.1996.0863

J. Bonini and M. Berthillier, Méthodes en dynamique non-linéaire des rotors pour l'´ etude du comportement d'un moteur d'avion. Revue Française de Mécanique, pp.221-226, 1999.

M. Borri, G. L. Ghiringhelli, M. Lanz, P. Mantegazza, and T. Merlini, Dynamic response of mechanical systems by a weak hamiltonian formulation, Computers & Structures, vol.20, pp.1-3495, 1985.

R. Bulirsch, F. Montrone, and H. J. Pesch, Abort landing in the presence of windshear as a minimax optimal control problem, part 2: Multiple shooting and homotopy, Journal of Optimization Theory and Applications, vol.36, issue.2
DOI : 10.1007/BF00940625

T. M. Cameron and J. H. Griffin, An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems, Journal of Applied Mechanics, vol.56, issue.1, pp.149-154, 1989.
DOI : 10.1115/1.3176036

URL : https://hal.archives-ouvertes.fr/hal-01333697

R. S. Chancellor, R. M. Alexander, and S. T. Noah, Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos, Journal of Vibration and Acoustics, vol.118, issue.3, pp.375-383, 1996.
DOI : 10.1115/1.2888193

C. S. Chen, S. Natsiavas, and H. D. Nelson, Stability Analysis and Complex Dynamics of a Gear-Pair System Supported by a Squeeze Film Damper, Journal of Vibration and Acoustics, vol.119, issue.1, pp.85-88, 1997.
DOI : 10.1115/1.2889691

C. S. Chen, S. Natsiavas, and H. D. Nelson, Coupled Lateral-Torsional Vibration of a Gear-Pair System Supported by a Squeeze Film Damper, Journal of Vibration and Acoustics, vol.120, issue.4, pp.860-867, 1998.
DOI : 10.1115/1.2893912

W. J. Chen-cheung, S. H. Chen, and S. L. Lau, Energy analysis to the design or rotor-bearing systems Application of the incremental harmonic balance method to cubic non-linearity systems, Journal of Engineering for Gas Turbines and Power Journal of Sound and Vibration, vol.11924, issue.1402, pp.411-417273, 1990.

D. W. Childs, Fractional-Frequency Rotor Motion Due to Nonsymmetric Clearance Effects, Journal of Engineering for Power, vol.104, issue.3, pp.533-541, 1982.
DOI : 10.1115/1.3227312

M. Chinta and A. B. Palazzolo, STABILITY AND BIFURCATION OF ROTOR MOTION IN A MAGNETIC BEARING, Journal of Sound and Vibration, vol.214, issue.5, pp.793-803, 1998.
DOI : 10.1006/jsvi.1998.1549

S. K. Choi and S. T. Noah, Mode-Locking and Chaos in a Jeffcott Rotor With Bearing Clearances, Journal of Applied Mechanics, vol.61, issue.1, pp.131-138, 1994.
DOI : 10.1115/1.2901387

Y. S. Choi and C. Y. Bae, Nonlinear dynamic analysis of partial rotor rub with experimental observations, Proceedings of the DETC, number DETC2001/VIB- 21634 in ASME 2001 Design Engineering Technical Conferences, 2001.

Y. S. Choi and S. T. Noah, Nonlinear Steady-State Response of a Rotor-Support System, Journal of Vibration Acoustics Stress and Reliability in Design, vol.109, issue.3, pp.255-261, 1987.
DOI : 10.1115/1.3269429

A. Choudhury and N. Tandon, A Theoretical Model to Predict Vibration Response of Rolling Bearings to Distributed Defects Under Radial Load, Journal of Vibration and Acoustics, vol.120, issue.1, pp.214-220, 1998.
DOI : 10.1115/1.2893808

F. Chu and Y. Tang, STABILITY AND NON-LINEAR RESPONSES OF A ROTOR-BEARING SYSTEM WITH PEDESTAL LOOSENESS, Journal of Sound and Vibration, vol.241, issue.5, pp.879-893, 2001.
DOI : 10.1006/jsvi.2000.3341

F. Chu and Z. Zhang, BIFURCATION AND CHAOS IN A RUB-IMPACT JEFFCOTT ROTOR SYSTEM, Journal of Sound and Vibration, vol.210, issue.1, pp.1-18, 1998.
DOI : 10.1006/jsvi.1997.1283

R. J. Comparin and R. Singh, Non-linear frequency response characteristics of an impact pair, Journal of Sound and Vibration, vol.134, issue.2, pp.259-290, 1989.
DOI : 10.1016/0022-460X(89)90652-4

R. D. Cook, D. S. Malkus, and M. E. Plesha, Concepts and applications of finite element analysis, 1989.

R. R. , C. Jr, and M. C. Bampton, Coupling of substructures for dynamic analyses., AIAA Journal, vol.6, issue.7, pp.1313-1319, 1968.
DOI : 10.2514/3.4741

J. M. Demul, J. M. Vree, and D. A. Maas, Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction???Part I: General Theory and Application to Ball Bearings, Journal of Tribology, vol.111, issue.1, pp.142-148, 1989.
DOI : 10.1115/1.3261864

J. M. Demul, J. M. Vree, and D. A. Maas, Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction???Part II: Application to Roller Bearings and Experimental Verification, Journal of Tribology, vol.111, issue.1, pp.149-155, 1989.
DOI : 10.1115/1.3261865

E. H. Dowell, The behavior of a linear, damped modal system with a non-linear spring-mass-dry friction damper system attached, Journal of Sound and Vibration, vol.89, issue.1, pp.65-83, 1983.
DOI : 10.1016/0022-460X(83)90911-2

J. Dugundji and J. H. , Some analysis methods for rotating systems with periodic coefficients, AIAA Journal, vol.21, issue.6, pp.890-897, 1983.
DOI : 10.2514/3.8167

F. F. Ehrich, Spontaneous Sidebanding in High Speed Rotordynamics, in Rotating Machinery and Vehicle Dynamics, pp.25-31, 1991.
DOI : 10.1115/1.2930291

F. F. Ehrich, The Dynamic Stability of Rotor/Stator Radial Rubs in Rotating Machinery, Journal of Engineering for Industry, vol.91, issue.4, pp.1025-1028, 1969.
DOI : 10.1115/1.3591743

F. F. Ehrich, Sum and Difference Frequencies in Vibration of High Speed Rotating Machinery, Journal of Engineering for Industry, vol.94, issue.1, pp.181-184, 1972.
DOI : 10.1115/1.3428109

F. F. Ehrich, High Order Subharmonic Response of High Speed Rotors in Bearing Clearance, Journal of Vibration Acoustics Stress and Reliability in Design, vol.110, issue.1, pp.9-16, 1988.
DOI : 10.1115/1.3269488

F. F. Ehrich, Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics, Journal of Vibration and Acoustics, vol.113, issue.1, pp.50-56, 1991.
DOI : 10.1115/1.2930154

F. 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, 1999.

F. F. Ehrich and J. J. Connor, Stator Whirl With Rotors in Bearing Clearance, Journal of Engineering for Industry, vol.89, issue.3, pp.381-390, 1967.
DOI : 10.1115/1.3610057

D. J. Ewins, Modal Testing: Theory and Practice, Journal of Vibration Acoustics Stress and Reliability in Design, vol.108, issue.1, 1984.
DOI : 10.1115/1.3269294

N. S. Feng and E. J. Hahn, Rolling element bearing non-linearity effects Ferri. On the equivalence of the incremental harmonic balance method and the harmonic balance ? Newton-Raphson method, Number 2000-GT-391 in Proceedings of ASME TURBOEXPO 2000, pp.455-456, 1986.

A. A. Ferri and E. H. Dowell, The behavior of a linear, damped modal system with a non-linear spring-mass???dry friction damper system attached, part II, Journal of Sound and Vibration, vol.101, issue.1, pp.55-74, 1985.
DOI : 10.1016/S0022-460X(85)80038-9

M. I. Friswell, J. E. Penny, and S. D. Garvey, THE APPLICATION OF THE IRS AND BALANCED REALIZATION METHODS TO OBTAIN REDUCED MODELS OF STRUCTURES WITH LOCAL NON-LINEARITIES, Journal of Sound and Vibration, vol.196, issue.4, pp.453-468, 1996.
DOI : 10.1006/jsvi.1996.0495

G. Frulla, Rigid rotor dynamic stability using Floquet theory, European Journal of Mechanics - A/Solids, vol.19, issue.1, pp.139-150, 2000.
DOI : 10.1016/S0997-7538(00)00151-0

R. Ganesan, Nonlinear Vibrations and Stability of a Rotor-Bearing System With Nonsymmetric Clearances, Journal of Engineering for Gas Turbines and Power, vol.119, issue.2, pp.418-424, 1997.
DOI : 10.1115/1.2815591

C. Gasquet and P. Witomski, Analyse de Fourier et applications. Filtrage, Calcul numrique, 1990.

G. Genta, A fast modal technique for the computation of the Campbell diagram of multi-degree-of-freedom rotors, Journal of Sound and Vibration, vol.155, issue.3, pp.385-402, 1992.
DOI : 10.1016/0022-460X(92)90708-6

M. Geradin and D. Rixen, Théorie des vibrations. ApplicationàApplication`Applicationà la dynamique des structures, 1992.

C. Gruber and W. Benoit, Mécanique générale. Presses polytechniques et universitaires romandes, 1998.

T. A. Harris, Rolling bearing analysis, 2001.

L. Houpert, An Engineering Approach to Hertzian Contact Elasticity???Part I, Journal of Tribology, vol.123, issue.3, pp.582-588, 2001.
DOI : 10.1115/1.1308043

L. Houpert, An Engineering Approach to Non-Hertzian Contact Elasticity???Part II, Journal of Tribology, vol.123, issue.3, pp.589-594, 2001.
DOI : 10.1115/1.1308042

C. S. Hsu, Impulsive Parametric Excitation: Theory, Journal of Applied Mechanics, vol.39, issue.2, pp.551-558, 1972.
DOI : 10.1115/1.3422715

W. Hu, H. Miah, and E. J. Hahn, A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings, Tribology International, vol.33, issue.3-4, pp.197-204, 2000.
DOI : 10.1016/S0301-679X(00)00027-X

M. Imregun and D. J. Ewins, Complex modes ? Origins and limits, Proceedings of the 13th IMAC, 1995.

Y. Ishida, Nonlinear Vibrations and Chaos in Rotordynamics, JSME international journal. Ser. C, Dynamics, control, robotics, design and manufacturing, vol.37, issue.2, pp.237-245, 1994.
DOI : 10.1299/jsmec1993.37.237

A. N. Jean and H. D. Nelson, Periodic response investigation of large order non-linear rotordynamic systems using collocation, Journal of Sound and Vibration, vol.143, issue.3, pp.473-489, 1990.
DOI : 10.1016/0022-460X(90)90737-K

A. N. Jean and T. N. Shiau, A reduction method for stability and dynamic response analysis of nonlinear mechanical systems. Number 93-GT-61 in International Gas Turbine and Aeroengine Congress and Exposition, pp.1-6, 1993.

A. Kahraman and G. W. Blankenship, Experiments on Nonlinear Dynamic Behavior of an Oscillator With Clearance and Periodically Time-Varying Parameters, Journal of Applied Mechanics, vol.64, issue.1, pp.217-226, 1997.
DOI : 10.1115/1.2787276

Y. B. Kim, Multiple harmonic balance method for aperiodic vibration of a piecewiselinear system, Journal of Applied Mechanics, vol.61, pp.131-138, 1994.

Y. B. Kim and S. T. Noah, Bifurcation analysis for a modified Jeffcott rotor with bearing clearances, Nonlinear Dynamics, vol.19, issue.No. 446, pp.221-241, 1990.
DOI : 10.1007/BF01858295

Y. B. Kim and S. T. Noah, Stability and Bifurcation Analysis of Oscillators With Piecewise-Linear Characteristics: A General Approach, Journal of Applied Mechanics, vol.58, issue.2, pp.545-553, 1991.
DOI : 10.1115/1.2897218

Y. B. Kim, S. T. Noah, and Y. S. Choi, Periodic response of multi-disk rotors with bearing clearances, Journal of Sound and Vibration, vol.144, issue.3, pp.381-395, 1991.
DOI : 10.1016/0022-460X(91)90558-2

Y. B. Kim and S. T. Noah, QUASI-PERIODIC RESPONSE AND STABILITY ANALYSIS FOR A NON-LINEAR JEFFCOTT ROTOR, Journal of Sound and Vibration, vol.190, issue.2, pp.239-253, 1996.
DOI : 10.1006/jsvi.1996.0059

M. Lalanne and G. Ferraris, Rotordynamics prediction in engineering, 1990.

C. H. Lamarque and O. Janin, Mechanical systems with impacts: comparison of several numerical methods, Proceedings of the DETC, number DETC99/VIB- 8347 in ASME Design Engineering Technical Conferences, pp.1-11, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00814950

S. L. Lau and W. S. Zhang, Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method, Journal of Applied Mechanics, vol.59, issue.1, pp.153-160, 1992.
DOI : 10.1115/1.2899421

J. L. Lawen and G. T. Flowers, Interaction Dynamics Between a Flexible Rotor and an Auxiliary Clearance Bearing, Journal of Vibration and Acoustics, vol.121, issue.2, pp.183-189, 1999.
DOI : 10.1115/1.2893962

Y. S. Lee and C. W. Lee, Modelling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems, Journal of Sound and Vibration, vol.224, issue.1, pp.17-32, 1999.
DOI : 10.1006/jsvi.1997.1301

A. Y. Leung and S. K. Chui, Non-linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method, Journal of Sound and Vibration, vol.181, issue.4, pp.619-633, 1995.
DOI : 10.1006/jsvi.1995.0162

A. Y. Leung and T. C. Fung, Construction of chaotic regions, Journal of Sound and Vibration, vol.131, issue.3, pp.445-455, 1985.
DOI : 10.1016/0022-460X(89)91004-3

N. T. Liao and J. F. Lin, A New Method for the Analysis of Deformation and Load in a Ball Bearing With Variable Contact Angle, Journal of Mechanical Design, vol.123, issue.2, pp.304-312, 2001.
DOI : 10.1115/1.1357163

C. Y. Liaw and C. G. Koh, Dynamic Stability and Chaos of System with Piecewise Linear Stiffness, Journal of Engineering Mechanics, vol.119, issue.8, pp.1542-1557, 1993.
DOI : 10.1061/(ASCE)0733-9399(1993)119:8(1542)

F. H. Ling, Quasi-periodic solutions calculated with the simple shooting technique, Journal of Sound and Vibration, vol.144, issue.2, pp.293-304, 1991.
DOI : 10.1016/0022-460X(91)90750-E

K. H. Low, COMMENTS ON ???AN ASSESSMENT OF TIME INTEGRATION SCHEMES FOR NON-LINEAR DYNAMIC EQUATIONS???, Journal of Sound and Vibration, vol.201, issue.2, pp.256-257, 1997.
DOI : 10.1006/jsvi.1996.0698

G. W. Luo and J. H. Xie, HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM, Journal of Sound and Vibration, vol.213, issue.3, pp.391-408, 1998.
DOI : 10.1006/jsvi.1997.1361

R. H. Mac and . Neal, A hybrid method of component mode synthesis, Computers & Structures, vol.1, pp.581-601, 1971.

L. Meirovitch, Principles and techniques of vibrations, 1997.

G. Meng and R. Gasch, Stability and Stability Degree of a Cracked Flexible Rotor Supported on Journal Bearings, Journal of Vibration and Acoustics, vol.122, issue.2, pp.116-125, 2000.
DOI : 10.1115/1.568448

P. Metallidis and S. Natsiavas, Dynamics of a continuous system with clearance and motion limiting stops, Proceedings of the DETC, number DETC99/VIB-8184 in ASME Design Engineering Technical Conferences, pp.1-9, 1999.

B. Mevel and J. L. Guyader, Routes To Chaos In Ball Bearings, Journal of Sound and Vibration, vol.162, issue.3, pp.471-487, 1993.
DOI : 10.1006/jsvi.1993.1134

URL : https://hal.archives-ouvertes.fr/hal-00414902

J. S. Mitchell, Introduction to machinery analysis and monitoring. Pennwell Books, 1993.

A. Muszynska, FORWARD AND BACKWARD PRECESSION OF A VERTICAL ANISOTROPICALLY SUPPORTED ROTOR, Journal of Sound and Vibration, vol.192, issue.1, pp.207-222, 1996.
DOI : 10.1006/jsvi.1996.0184

S. Narayanan and P. Sekar, A FREQUENCY DOMAIN BASED NUMERIC???ANALYTICAL METHOD FOR NON-LINEAR DYNAMICAL SYSTEMS, Journal of Sound and Vibration, vol.211, issue.3, pp.409-424, 1998.
DOI : 10.1006/jsvi.1997.1319

C. Nataraj and H. D. Nelson, Periodic Solutions in Rotor Dynamic Systems With Nonlinear Supports: A General Approach, Journal of Vibration Acoustics Stress and Reliability in Design, vol.111, issue.2, pp.187-193, 1989.
DOI : 10.1115/1.3269840

S. Natsiavas, Periodic response and stability of oscillators with symmetric trilinear restoring force, Journal of Sound and Vibration, vol.134, issue.2, pp.315-331, 1989.
DOI : 10.1016/0022-460X(89)90654-8

A. H. Nayfeh and B. Balachandran, Applied nonlinear dynamics, 1995.
DOI : 10.1002/9783527617548

A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, 1979.

D. Nelias, P. Sainsot, and L. Flamand, Power Loss of Gearbox Ball Bearing Under Axial and Radial Loads??, Tribology Transactions, vol.48, issue.1, pp.83-90, 1994.
DOI : 10.1115/1.3453074

D. Nelias and T. Yoshioka, Location of an acoustic emission source in a radially loaded deep groove ball-bearing, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol.2, issue.1, pp.33-45, 1998.
DOI : 10.1243/1350650981541877

S. Okamoto, M. Sakata, K. Kimura, and H. Ohnabe, Vibration analysis of a high speed and light weight rotor system subjected to a pitching or turning motion, Journal of Sound and Vibration, vol.184, issue.5, pp.887-906, 1995.
DOI : 10.1006/jsvi.1995.0351

C. Padmanabhan and R. Singh, Analysis of periodically excited non-linear systems by a parametric continuation technique, Journal of Sound and Vibration, vol.184, issue.1, pp.35-58, 1995.
DOI : 10.1006/jsvi.1995.0303

S. Park, Development and applications of finite elements in time domain, 1996.

C. Pierre, A. A. Ferri, E. H. Dowell, S. A. Teukolsky, W. T. Vetterling et al., Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method, Journal of Applied Mechanics, vol.52, issue.4, pp.958-964, 1992.
DOI : 10.1115/1.3169175

A. Raghothama and D. Narayanan, BIFURCATION AND CHAOS IN GEARED ROTOR BEARING SYSTEM BY INCREMENTAL HARMONIC BALANCE METHOD, Journal of Sound and Vibration, vol.226, issue.3, pp.469-492, 1999.
DOI : 10.1006/jsvi.1999.2264

A. Raghothama and D. Narayanan, NON-LINEAR DYNAMICS OF A TWO-DIMENSIONAL AIRFOIL BY INCREMENTAL HARMONIC BALANCE METHOD, Journal of Sound and Vibration, vol.226, issue.3, pp.493-517, 1999.
DOI : 10.1006/jsvi.1999.2260

C. Rao, R. B. Bhat, and G. Xistris, Experimental verification of simultaneous forward and backward whirling at different points of a Jeffcott rotor supported on identical journal bearings, Journal of Sound and Vibration, vol.198, issue.3, pp.379-388, 1996.

Y. Ren and C. F. Beards, On Application of the Harmonic Balance Method to Structures Containing One Non-Linear Element, Journal of Sound and Vibration, vol.175, issue.5, pp.705-710, 1994.
DOI : 10.1006/jsvi.1994.1560

R. Riff and M. Baruch, Time finite element discretization of Hamilton's law of varying action, American Institute of Aeronautics and Astronautics Journal, vol.22, issue.9, pp.1310-1318, 1984.

T. J. Royston and R. Singh, EXPERIMENTAL STUDY OF A MECHANICAL SYSTEM CONTAINING A LOCAL CONTINUOUS STIFFNESS NON-LINEARITY UNDER PERIODIC EXCITATION AND A STATIC LOAD, Journal of Sound and Vibration, vol.198, issue.3, pp.279-298, 1996.
DOI : 10.1006/jsvi.1996.0570

S. Saito, Calculation of Nonlinear Unbalance Response of Horizontal Jeffcott Rotors Supported by Ball Bearings With Radial Clearances, Journal of Vibration Acoustics Stress and Reliability in Design, vol.107, issue.4, pp.416-420, 1985.
DOI : 10.1115/1.3269282

M. Sakata, K. Kimura, S. Okamoto, and K. Oikawa, Vibration analysis of a high speed and light weight rotor system subjected to a pitching or turning motion, Journal of Sound and Vibration, vol.184, issue.5, pp.871-885, 1995.
DOI : 10.1006/jsvi.1995.0350

P. Sekar, Chaotic vibrations in systems with contact and impact nonlinearities, 1995.

C. Semler, W. C. Gentleman, and M. P. , NUMERICAL SOLUTIONS OF SECOND ORDER IMPLICIT NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS, Journal of Sound and Vibration, vol.195, issue.4, pp.553-574, 1996.
DOI : 10.1006/jsvi.1996.0445

R. Seydel, Practical bifurcation and stability analysis. From equilibrium to chaos, 1994.

T. N. Shiau and A. N. Jean, Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics, Journal of Vibration and Acoustics, vol.112, issue.4, pp.501-507, 1990.
DOI : 10.1115/1.2930135

T. N. Shiau and A. N. Jean, Nonlinear Transient Analysis of Large Rotordynamic Systems, Journal of Applied Mechanics, vol.58, issue.2, pp.596-598, 1991.
DOI : 10.1115/1.2897233

T. E. Simkins, Finite Elements for Initial Value Problems in Dynamics, AIAA Journal, vol.19, issue.10, pp.1357-1362, 1981.
DOI : 10.2514/3.60069

Y. C. Sin, Bearing nonlinearity and stability analysis in high speed machining, Journal of Engineering for Industry. Series B, vol.114, pp.23-30, 1992.

J. J. Slotine and W. T. Lee, Applied nonlinear control, 1991.

C. V. Smith and . Jr, Remarks on a Comment by C.D. Bailey, AIAA Journal, vol.22, issue.8, pp.1178-1179, 1984.
DOI : 10.2514/3.48558

. Gaffney, Blade loss transient dynamic analysis of turbomachinery, American Institute of Aeronautics and Astronautics Journal, vol.21, issue.8, pp.1134-1138, 1983.

H. B. Stewart, J. M. Thompson, Y. Ueda, and A. N. Lansbury, Optimal escape from potential wells-patterns of regular and chaotic bifurcation, Physica D: Nonlinear Phenomena, vol.85, issue.1-2, pp.259-295, 1995.
DOI : 10.1016/0167-2789(95)00172-Z

J. Stoer and R. Bulirsch, Introduction to numerical analysis, 1980.

Y. T. Su, M. H. Lin, and M. S. Lee, The Effects of Surface Irregularities on Roller Bearing Vibrations, Journal of Sound and Vibration, vol.165, issue.3, pp.455-466, 1993.
DOI : 10.1006/jsvi.1993.1270

R. Subbiah, A. S. Kumar, and T. S. Sankar, Transient Dynamic Analysis of Rotors Using the Combined Methodologies of Finite Elements and Transfer Matrix, Journal of Applied Mechanics, vol.55, issue.2, pp.448-452, 1988.
DOI : 10.1115/1.3173697

R. Subbiah and N. F. Rieger, On the Transient Analysis of Rotor-Bearing Systems, Journal of Vibration Acoustics Stress and Reliability in Design, vol.110, issue.4, pp.515-520, 1988.
DOI : 10.1115/1.3269559

P. Sundararajan, S. T. Noah, and S. T. Singh, AN ALGORITHM FOR RESPONSE AND STABILITY OF LARGE ORDER NON-LINEAR SYSTEMS ??? APPLICATION TO ROTOR SYSTEMS, Journal of Sound and Vibration, vol.214, issue.4, pp.695-7239, 1997.
DOI : 10.1006/jsvi.1998.1614

URL : https://hal.archives-ouvertes.fr/hal-01353830

C. S. Sunnersjo, Rolling bearing vibrations???The effects of geometrical imperfections and wear, Journal of Sound and Vibration, vol.98, issue.4, pp.455-474, 1985.
DOI : 10.1016/0022-460X(85)90256-1

N. Tandon and A. Choudhury, AN ANALYTICAL MODEL FOR THE PREDICTION OF THE VIBRATION RESPONSE OF ROLLING ELEMENT BEARINGS DUE TO A LOCALIZED DEFECT, Journal of Sound and Vibration, vol.205, issue.3, pp.275-292, 1997.
DOI : 10.1006/jsvi.1997.1031

B. Tchamwa, T. Conway, and C. Wielgosz, An explicit scheme for structural dynamics analysis, Proceedings of the DETC, number DETC99/VIB-8160 in ASME Design Engineering Technical Conferences, pp.1-8, 1999.

S. Theodossiades and S. Natsiavas, NON-LINEAR DYNAMICS OF GEAR-PAIR SYSTEMS WITH PERIODIC STIFFNESS AND BACKLASH, Journal of Sound and Vibration, vol.229, issue.2, pp.287-310, 2000.
DOI : 10.1006/jsvi.1999.2490

J. M. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, Computers in Physics, vol.4, issue.5, 1986.
DOI : 10.1063/1.4822949

M. Tiwari, K. Gupta, and O. Prakash, DYNAMIC RESPONSE OF AN UNBALANCED ROTOR SUPPORTED ON BALL BEARINGS, Journal of Sound and Vibration, vol.238, issue.5, pp.757-779, 2000.
DOI : 10.1006/jsvi.1999.3108

M. Tiwari, K. Gupta, and O. Prakash, EFFECT OF RADIAL INTERNAL CLEARANCE OF A BALL BEARING ON THE DYNAMICS OF A BALANCED HORIZONTAL ROTOR, Journal of Sound and Vibration, vol.238, issue.5, pp.723-756, 2000.
DOI : 10.1006/jsvi.1999.3109

A. P. Urgueira, N. M. Maia, and R. A. Almeida, On the dynamic properties of reduced systems in structural coupling, 17th IMAC, pp.1445-1450, 1999.

E. L. Van-de-vorst, R. H. Fey, A. De-kraker, and D. H. Van-campen, Steady-state behaviour of nonlinear flexible rotor-bearing systems: Part I ? An efficient numerical analysis method. Machine Vibration, pp.138-145, 1995.

E. L. Van-de-vorst, R. H. Fey, A. De-kraker, and D. H. Van-campen, Steady-state behaviour of nonlinear flexible rotor-bearing systems: Part II ? Application: Influence of cavitation modelling, Machine Vibration, pp.146-155, 1995.

R. Van-dooren, COMMENTS ON ???A FREQUENCY DOMAIN BASED NUMERIC-ANALYTICAL METHOD FOR NON-LINEAR DYNAMICAL SYSTEMS???, Journal of Sound and Vibration, vol.226, issue.4, pp.799-805, 1999.
DOI : 10.1006/jsvi.1999.2288

J. M. Vance, Rotordynamcis of turbomachinery, 1988.

G. , V. Groll, and D. J. Ewins, Frequency domain analysis in rotor/stator contact problems, Proceedings of the IIAV, number paper 660 in 7th international conference on Sound and Vibration, Garmisch-Partenkirchen, pp.1-8, 2000.

G. , V. Groll, and D. J. Ewins, On the dynamics of windmilling in aero-engines, 7th International Conference on Vibrations of Rotating Machinery, pp.721-730, 2000.

G. , V. Groll, and D. J. Ewins, The harmonic balance method with arc-length continuation in rotor/stator contact problems, Journal of Sound and Vibration, vol.241, issue.2, pp.223-233, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01333704

L. Vu-quoc, X. Zhang, and L. Lesburg, A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation, Journal of Applied Mechanics, vol.67, issue.2, pp.363-371, 2000.
DOI : 10.1115/1.1305334

Y. Wang, Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time, Journal of Sound and Vibration, vol.185, issue.1, pp.155-170, 1995.
DOI : 10.1006/jsvi.1994.0369

URL : https://hal.archives-ouvertes.fr/hal-01333696

Y. Wang, Prediction of Periodic Response of Rotor Dynamic Systems With Nonlinear Supports, Journal of Vibration and Acoustics, vol.119, issue.3, pp.346-353, 1997.
DOI : 10.1115/1.2889730

Z. Wu and Y. Chen, Prediction for the rub-impact phenomena in rotor systems, Proceedings of the DETC, number DETC2001/VIB-21633 in ASME Design Engineering Technical Conferences, 2001.

G. Xie and Y. K. Lou, Alternating frequency/coefficient (AFC) technique in the harmonic balance method, International Journal of Non-Linear Mechanics, vol.31, issue.4, pp.517-529, 1996.
DOI : 10.1016/0020-7462(95)00066-6

G. Xie and Y. K. Lou, Alternating frequency/coefficient (AFC) technique in the trigonometric collocation method, International Journal of Non-Linear Mechanics, vol.31, issue.4, pp.531-545, 1996.
DOI : 10.1016/0020-7462(96)00003-0

Y. M. Xie, AN ASSESSMENT OF TIME INTEGRATION SCHEMES FOR NON-LINEAR DYNAMIC EQUATIONS, Journal of Sound and Vibration, vol.192, issue.1, pp.321-331, 1996.
DOI : 10.1006/jsvi.1996.0190

T. Yamamoto and Y. Ishida, Linear and nonlinear rotordynamics [155] E. Yhland. A linear theory of vibrations caused by ball bearings with form errors operating at moderate speed, Journal of Tribology, vol.114, pp.348-359, 1992.

J. Y. Zhao, I. W. Linnett, and L. J. Mclean, Stability and Bifurcation of Unbalanced Response of a Squeeze Film Damped Flexible Rotor, Journal of Tribology, vol.116, issue.2, pp.361-368, 1994.
DOI : 10.1115/1.2927236

J. Y. Zhao, I. W. Linnett, and L. J. Mclean, Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor, Journal of Vibration and Acoustics, vol.116, issue.3, pp.357-363, 1994.
DOI : 10.1115/1.2930436

G. T. Zheng, Vibration of a Rotor System With a Switching Crack and Detection of the Crack, Journal of Engineering for Gas Turbines and Power, vol.120, issue.1, pp.149-154, 1998.
DOI : 10.1115/1.2818068

T. Zheng and N. Hasebe, An Efficient Analysis of High-Order Dynamical System with Local Nonlinearity, Journal of Vibration and Acoustics, vol.121, issue.3, pp.408-416, 1999.
DOI : 10.1115/1.2893995

T. Zheng and N. Hasebe, Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System, Journal of Applied Mechanics, vol.67, issue.3, pp.485-495, 2000.
DOI : 10.1115/1.1286208

O. C. Zienkiewicz and R. L. Taylor, The finite element method Basic formulation and linear problems, 1994.

E. S. Zorzi and H. D. Nelson, Finite Element Simulation of Rotor-Bearing Systems With Internal Damping, Journal of Engineering for Power, vol.99, issue.1, pp.71-76, 1977.
DOI : 10.1115/1.3446254