V. Arnold, Mathematical Methods of Calssical Mechanics, 1978.

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

O. A. Bauchau, A solution of the eigenproblem for undamped gyroscopic systems with the Lanczos algorithm, International Journal for Numerical Methods in Engineering, vol.7, issue.9, pp.1705-1713
DOI : 10.1002/nme.1620230910

C. E. Beevers, Some Continuous Dependence Results in the Linear Dynamic Theory of Anisotropic Viscoelasticity, Journal de Mécanique, vol.14, issue.4, pp.640-651, 1975.

N. N. Bogolubov and I. A. , Mitropol'Skij, Les Méthodes asymptotiques en théorie des oscillations non linéaires, 1962.

H. Brezis, Analyse fonctionnelle, théorie et applications, 1993.

J. Casey and P. M. Naghdi, Physically NonLinear and Related Approximate Theories of Elasticity and their Invariance Properties, Archive for Rational Mechanics and Analysis, pp.59-82, 1985.

J. Casey and P. M. Naghdi, An invariant infinitesimal theory of motions superposed on a given motion, Archive for Rational Mechanics and Analysis, vol.76, issue.4, pp.355-391, 1985.
DOI : 10.1007/BF00249971

G. Chakraborty, A. K. Mallik, and H. Hatwl, Non-linear vibration of a travelling beam, International Journal of Non-Linear Mechanics, vol.34, issue.4, pp.345-655, 1999.
DOI : 10.1016/S0020-7462(98)00017-1

P. G. Ciarlet, Mathematical Elasticity, North-Holland, 1988.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1978.

B. D. Coleman and W. Noll, Foundations of Linear Viscoelasticity, Reviews of Modern Physics, vol.33, issue.2, pp.239-249, 1961.
DOI : 10.1103/RevModPhys.33.239

R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 1992.

C. Desceliers, Dynamique non linéaire en déplacements finis des structures tridimensionnelles viscoélastiques en rotation, Thése de Doctorat, 2001.

S. Dubigeon and J. C. Michon, Modes for deformable periodic cyclic symmetric systems driven in uniform rotation by a flexible shaft, Journal of Sound and Vibration, vol.106, issue.1, pp.53-70, 1986.
DOI : 10.1016/S0022-460X(86)80174-2

G. Duvaut and J. Lions, Les inéquations en mécanique et en physique, 1972.

C. Desceliers and C. Soize, Second revised version [18] E. Esmailzadeh, G. Nakhaie-Jazar, Periodic behavior of a Cantilever Beam with End Mass Subjected to Harmonic Base Excitation, International Journal of Non-Linear Mechanics Int. J. Non-Linear Mechanics, vol.4, issue.33, pp.567-577, 1998.

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

K. K. Gupta, Development of a unified numerical procedure for free vibration analysis of structures, International Journal for Numerical Methods in Engineering, vol.7, issue.2, pp.187-198, 1981.
DOI : 10.1002/nme.1620170204

A. E. Green, R. S. Rivlin, and R. T. Shield, General Theory of Small Elastic Deformations Superposed on Finite Elastic Deformations, Archive for Rational Mechanics and Analysis, vol.211, pp.128-154, 1951.

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

G. Jacquet-richardet, G. Ferraris, and P. Rieutord, FREQUENCIES AND MODES OF ROTATING FLEXIBLE BLADED DISC-SHAFT ASSEMBLIES: A GLOBAL CYCLIC SYMMETRY APPROACH, Journal of Sound and Vibration, vol.191, issue.5, pp.901-915, 1996.
DOI : 10.1006/jsvi.1996.0162

L. Jézéquel and C. H. Lamarque, Analysis of non-linear dynamical systems by the normal form theory, Journal of Sound and Vibration, vol.149, issue.3, pp.429-459, 1991.
DOI : 10.1016/0022-460X(91)90446-Q

P. B. Kahn and Y. Zarmi, Nonlinear Dynamics Exploration Through Normal Forms, 1998.

M. J. Kruse and C. Pierre, An Experimental Investigation of Vibration Localization in Bladed Disks, Part I : Free Response, Part II : Forced Response, ASME Paper 97-GT-502-Proceedings of ASME Gas Turbine Conference, 1997.

K. R. Meyer and G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 1992.
DOI : 10.1007/978-1-4757-4073-8

A. Y. Leung and Q. C. Zhang, HIGHER ORDER NORMAL FORM AND PERIOD AVERAGING, Journal of Sound and Vibration, vol.217, issue.5, pp.795-806, 1998.
DOI : 10.1006/jsvi.1998.1752

J. Mandel, Cours de Mécanique des milieux continus, Tomes II, Mécanique des solides, 1966.

R. J. Mcdonald, J. Murdock, and N. N. Sri, Non-autonomous normal forms for Hamiltonian systems, Dynamics and Stability of Systems, vol.14, issue.4, pp.357-384, 1999.
DOI : 10.1080/026811199281949

W. Nagata and N. S. Namachchivaya, Bifurcations in gyroscopic systems with an application to rotating shafts, Proc. R. Soc. Lond. A, pp.543-585, 1998.
DOI : 10.1098/rspa.1998.0174

A. H. Nayfeh, Method of Normal Forms, 1993.
DOI : 10.1002/9783527635801

A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics, 1995.
DOI : 10.1002/9783527617548

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

O. M. O-'reilly and J. S. Turcotte, Elastic Rods with Moderate Rotation, Journal of Elasticity, vol.48, issue.3, pp.193-216, 1997.
DOI : 10.1023/A:1007456117487

D. Qian and J. S. Hansen, A substructure synthesis method for non-symmetric viscoelastic systems, Journal of Sound and Vibration, vol.185, issue.4, pp.627-641, 1995.
DOI : 10.1006/jsvi.1995.0405

W. Wang and J. Kirkhope, New Eigensolutions and Modal Analysis for Gyroscopic, Rotor Systems, Part Journal of Sound and Vibration, vol.1, issue.1752, pp.159-170, 1994.

W. Wang and J. Kirkhope, New Eigensolutions And Modal Analysis For Gyroscopic/rotor Systems, Part 2: Perturbation Analysis For Damped Systems, Journal of Sound and Vibration, vol.175, issue.2, pp.171-183, 1994.
DOI : 10.1006/jsvi.1994.1321

J. A. Wickert, TRANSIENT VIBRATION OF GYROSCOPIC SYSTEMS WITH UNSTEADY SUPERPOSED MOTION, Journal of Sound and Vibration, vol.195, issue.5, pp.797-807, 1996.
DOI : 10.1006/jsvi.1996.0462

A. Wineman and R. Kolberg, Response of beams of non-linear viscoelastic materials exhibiting strain-dependent stress relaxation, International Journal of Non-Linear Mechanics, vol.32, issue.5, pp.863-883
DOI : 10.1016/S0020-7462(96)00100-X

H. H. Yoo and S. H. Shin, VIBRATION ANALYSIS OF ROTATING CANTILEVER BEAMS, Journal of Sound and Vibration, vol.212, issue.5, pp.807-828, 1998.
DOI : 10.1006/jsvi.1997.1469

A. A. Zevin, On the theory of linear gyroscopic systems, Journal of Applied Mathematics and Mechanics, vol.60, issue.2, pp.227-232, 1996.
DOI : 10.1016/0021-8928(96)00029-9

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 1991.