R. Benamar, M. M. Bennouna, and R. G. White, The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part I: Simply supported and clamped-clamped beams, Journal of Sound and Vibration, vol.149, issue.2, pp.179-195, 1991.
DOI : 10.1016/0022-460X(91)90630-3

M. Amabili, F. Pellicano, and M. P. Pa, NONLINEAR VIBRATIONS OF SIMPLY SUPPORTED, CIRCULAR CYLINDRICAL SHELLS, COUPLED TO QUIESCENT FLUID, Journal of Fluids and Structures, vol.12, issue.7, pp.883-918, 1998.
DOI : 10.1006/jfls.1998.0173

M. Amabili, Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections, Journal of Sound and Vibration, vol.262, issue.4, pp.921-975, 2003.
DOI : 10.1016/S0022-460X(02)01051-9

W. Lacarbonara, A Theoretical and Experimental Investigation of Nonlinear Vibrations of Buckled Beams, 1997.

A. H. Nayfeh, J. F. Nayfeh, and D. T. Mook, On methods for continuous systems with quadratic and cubic nonlinearities, Nonlinear Dynamics, vol.89, issue.2, pp.145-162, 1992.
DOI : 10.1007/BF00118990

M. Pakdemirli, S. A. Nayfeh, and A. H. Nayfeh, Analysis of One-to-One Autoparametric Resonances in Cables ??? Discretization vs. Direct Treatment, Nonlinear Dynamics, vol.8, pp.65-83, 1995.
DOI : 10.1007/978-94-011-0367-1_4

A. H. Nayfeh and W. Lacarbonara, On the discretization of distributed-parameter systems with quadratic and cubic nonlinearities, Nonlinear Dynamics, vol.13, issue.3, pp.203-220, 1997.
DOI : 10.1023/A:1008253901255

A. H. Nayfeh, Reduced-order models of weakly non-linear spatially continuous systems, Nonlinear Dynamics, vol.16, issue.2, pp.105-125, 1998.
DOI : 10.1023/A:1008281121523

S. W. Shaw and C. Pierre, Normal Modes for Non-Linear Vibratory Systems, Journal of Sound and Vibration, vol.164, issue.1, pp.85-124, 1993.
DOI : 10.1006/jsvi.1993.1198

S. W. Shaw and C. Pierre, Normal Modes of Vibration for Non-Linear Continuous Systems, Journal of Sound and Vibration, vol.169, issue.3, pp.319-347, 1994.
DOI : 10.1006/jsvi.1994.1021

URL : https://hal.archives-ouvertes.fr/hal-01471098

R. M. Rosenberg, On Nonlinear Vibrations of Systems with Many Degrees of Freedom, Advances in Applied Mechanics, vol.9, pp.155-242, 1966.
DOI : 10.1016/S0065-2156(08)70008-5

A. F. Vakakis, L. I. Mikhlin, Y. V. Philipchuck, and A. A. , Zevin, Normal Modes and Localization in Nonlinear Systems, 1996.

L. Jezequel 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

URL : https://hal.archives-ouvertes.fr/hal-00814435

L. Jezequel and C. H. Lamarque, Nonlinear modal synthesis based on normal form theory, Proceedings of the Ninth International Modal Analysis Conference, pp.101-108, 1991.

A. H. Nayfeh and S. A. Nayfeh, On Nonlinear Modes of Continuous Systems, Journal of Vibration and Acoustics, vol.116, issue.1, pp.129-136, 1994.
DOI : 10.1115/1.2930388

R. H. Rand, A direct method for non-linear normal modes, International Journal of Non-Linear Mechanics, vol.9, issue.5, pp.363-368, 1974.
DOI : 10.1016/0020-7462(74)90021-3

A. F. Vakakis, NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW, Mechanical Systems and Signal Processing, vol.11, issue.1, pp.3-22, 1997.
DOI : 10.1006/mssp.1996.9999

URL : https://hal.archives-ouvertes.fr/hal-01354037

E. Peshek, C. Pierre, and S. W. Shaw, A NEW GALERKIN-BASED APPROACH FOR ACCURATE NON-LINEAR NORMAL MODES THROUGH INVARIANT MANIFOLDS, Journal of Sound and Vibration, vol.249, issue.5, pp.971-993, 2002.
DOI : 10.1006/jsvi.2001.3914

J. Guckenheimer and P. J. Holmes, Non-linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1986.

A. D. Brjuno, Analytical form of differential equations, Transactions of Moscow Mathematical Society, vol.25, pp.131-288, 1971.

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

F. Pellicano and F. Mastroddi, APPLICABILITY CONDITIONS OF A NON-LINEAR SUPERPOSITION TECHNIQUE, Journal of Sound and Vibration, vol.200, issue.1, pp.3-14, 1997.
DOI : 10.1006/jsvi.1996.0665

L. Morino, F. Mastroddi, and M. Cutroni, Lie transformation method for dynamical systems having chaotic behavior, Nonlinear Dynamics, vol.1, issue.8, pp.403-428, 1995.
DOI : 10.1007/BF00121106

A. H. Nayfeh, C. Chin, and S. A. Nayfeh, On Nonlinear Normal Modes of Systems With Internal Resonance, Journal of Vibration and Acoustics, vol.118, issue.3, pp.340-345, 1996.
DOI : 10.1115/1.2888188

E. Peshek and C. Pierre, A global methodology for the modal reduction of large non-linear systems containing quadratic and cubic non-linearities, Proceedings of DETC'97, 1997.

T. D. Burton and M. N. Hamdan, LETTER TO THE EDITOR: ON THE CALACULATION OF NON-LINEAR NORMAL MODES IN CONTINUOUS SYSTEMS, Journal of Sound and Vibration, vol.197, issue.1, pp.117-130, 1996.
DOI : 10.1006/jsvi.1996.0520

M. I. Qaisi, NON-LINEAR NORMAL MODES OF A CONTINUOUS SYSTEM, Journal of Sound and Vibration, vol.209, issue.4, pp.561-569, 1998.
DOI : 10.1006/jsvi.1997.1246

F. Pellicano and F. Mastroddi, Nonlinear dynamics of a beam on elastic foundation, Nonlinear Dynamics, vol.14, issue.4, pp.335-355, 1997.
DOI : 10.1023/A:1008297721253

C. Touz and !. , A normal form approach for non-linear normal modes, Internal Publication of the LMA

C. Touz-!-e and O. Thomas, Determination of non-linear normal modes for conservative systems, Proceedings of the Ninth ICSV, vol.70, 2002.

C. Touz-!-e and O. Thomas, Modes normaux non-lin! eaires de syst" emes continus, Proceedings of Congr" es Fran@ais de M! ecanique, 2003.

P. Manneville and L. S. Tuckerman, Phenomenological modelling of the first bifurcations of spherical Couette flow, Journal de Physique, vol.48, issue.9, pp.1461-1469, 1987.
DOI : 10.1051/jphys:019870048090146100

URL : https://hal.archives-ouvertes.fr/jpa-00210576

N. Boivin, C. Pierre, and S. W. Shaw, Non-linear modal analysis of structural systems featuring internal resonances, Journal of Sound and Vibration, vol.182, issue.2, pp.336-341, 1995.
DOI : 10.1006/jsvi.1995.0201

A. G. Haddow, A. D. Barr, and D. T. Mook, Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure, Journal of Sound and Vibration, vol.97, issue.3, pp.451-473, 1984.
DOI : 10.1016/0022-460X(84)90272-4

S. Sridhar, D. T. Mook, and A. H. Nayfeh, Non-linear resonances in the forced responses of plates, part 1: Symmetric responses of circular plates, Journal of Sound and Vibration, vol.41, issue.3, pp.359-373, 1975.
DOI : 10.1016/S0022-460X(75)80182-9

C. Touz-!-e, P. Lanchantin, O. Thomas, and A. Chaigne, Transferts d'! energie par couplage modal: ! etude d'un cas particulier, Proceedings of Sixi " eme Congr" es Fran@ais d'Acoustique, 2002.