A. H. Nayfeh, Nonlinear interactions: analytical, computational and experimental methods Wiley series in nonlinear science, 2000.

P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent structures, Dynamical systems and Symmetry, 1996.

B. F. Feeny and R. Kappagantu, ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS, Journal of Sound and Vibration, vol.211, issue.4, pp.607-616, 1998.
DOI : 10.1006/jsvi.1997.1386

B. F. Feeny, ON PROPER ORTHOGONAL CO-ORDINATES AS INDICATORS OF MODAL ACTIVITY, Journal of Sound and Vibration, vol.255, issue.5, pp.805-817, 2002.
DOI : 10.1006/jsvi.2001.4120

G. Kerschen and J. C. , PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION, Journal of Sound and Vibration, vol.249, issue.5, pp.849-865, 2002.
DOI : 10.1006/jsvi.2001.3930

M. Amabili, A. Sarkar, and M. P. Païdoussis, Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method, Journal of Fluids and Structures, vol.18, issue.2, pp.227-250, 2003.
DOI : 10.1016/j.jfluidstructs.2003.06.002

W. Z. Lin, K. H. Lee, P. Lu, S. P. Lim, and Y. C. Liang, THE RELATIONSHIP BETWEEN EIGENFUNCTIONS OF KARHUNEN???LO??VE DECOMPOSITION AND THE MODES OF DISTRIBUTED PARAMETER VIBRATION SYSTEM, Journal of Sound and Vibration, vol.256, issue.4, pp.791-799, 2002.
DOI : 10.1006/jsvi.2001.4223

Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, K. H. Lee et al., PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS???PART I: THEORY, Journal of Sound and Vibration, vol.252, issue.3, pp.527-544, 2002.
DOI : 10.1006/jsvi.2001.4041

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

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 nonlinear spatially continuous systems, Nonlinear Dynamics, vol.16, issue.2, pp.105-125, 1998.
DOI : 10.1023/A:1008281121523

C. Touzé, O. Thomas, and A. Chaigne, Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes, Journal of Sound and Vibration, vol.273, issue.1-2, p.20
DOI : 10.1016/j.jsv.2003.04.005

M. Amabili, F. Pellicano, and M. P. Païdoussis, 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

W. Lacarbonara, A theoretical and experimental investigation of nonlinear vibrations of buckled beams, polytechnic institute and state university, 1997.

H. N. Arafat and A. H. Nayfeh, Non-linear responses of suspended cables to primary resonance excitations, Journal of Sound and Vibration, vol.266, issue.2, pp.325-354, 2003.
DOI : 10.1016/S0022-460X(02)01393-7

A. F. Vakakis, L. I. Mikhlin, Y. V. Philipchuck, and A. A. Zevin, Normal modes and localization in nonlinear systems, 1996.

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

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

E. Pesheck, 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

M. E. King and A. F. Vakakis, An Energy-Based Formulation for Computing Nonlinear Normal Modes in Undamped Continuous Systems, Journal of Vibration and Acoustics, vol.116, issue.3, pp.332-340, 1994.
DOI : 10.1115/1.2930433

C. Touzé, A normal form approach for non-linear normal modes. Internal publication of the, LMA, vol.156, pp.15-38, 2003.

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

C. Touzé and O. Thomas, Determination of non-linear normal modes for conservative systems

M. Amabili, F. Pellicano, and M. P. Païdoussis, NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID, PART II: LARGE-AMPLITUDE VIBRATIONS WITHOUT FLOW, Journal of Sound and Vibration, vol.228, issue.5, pp.1103-1124, 1999.
DOI : 10.1006/jsvi.1999.2476

P. Ribeiro and M. Petyt, NON-LINEAR VIBRATION OF BEAMS WITH INTERNAL RESONANCE BY THE HIERARCHICAL FINITE-ELEMENT METHOD, Journal of Sound and Vibration, vol.224, issue.4, pp.591-624, 1999.
DOI : 10.1006/jsvi.1999.2193

E. Pesheck, Reduced-order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds, 2000.
URL : https://hal.archives-ouvertes.fr/tel-00361026

E. Pesheck and C. Pierre, A global methodology for the modal reduction of large nonlinear systems containing quadratic and cubic nonlinearities, Proc. of DETC'97, 1997.

M. Amabili and M. Pellegrini, Nonlinear vibrations of circular cylindrical panels, Proc. of the Second MIT Conference, pp.50-53, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01403853

N. Boivin, C. Pierre, and S. Shaw, Non-linear normal modes, invariance, and modal dynamics approximations of non-linear systems, Nonlinear Dynamics, vol.8, pp.315-346, 1995.

A. D. Brjuno, Analytical form of differential equations, Trans. Moscow Math. Soc, vol.25, pp.131-288, 1971.

J. Guckenheimer and P. J. Holmes, Non-linear oscillations, dynamical systems and bifurcation of vector fields, 1986.

P. Manneville, Dissipative structures and weak turbulence, 1990.
DOI : 10.1007/3-540-60188-0_59

R. Bouc and S. Bellizzi, Une nouvelle approche pour l'existence et le calcul des modes nonlinéaires, Internal publication of the LMA, vol.156, pp.38-58, 2003.