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

M. Amabili and M. P. Païdoussis, Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction, Applied Mechanics Reviews, vol.56, issue.4, pp.349-381, 2003.
DOI : 10.1115/1.1565084

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

M. Amabili, A. Sarkar, and M. P. Païdoussis, Chaotic vibrations of circular cylindrical shells: Galerkin versus reduced-order models via the proper orthogonal decomposition method, Journal of Sound and Vibration, vol.290, issue.3-5, pp.736-762, 2006.
DOI : 10.1016/j.jsv.2005.04.034

N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, Journal of Fluid Mechanics, vol.15, issue.-1, pp.115-173, 1988.
DOI : 10.1146/annurev.fl.13.010181.002325

M. F. Azeez and A. F. Vakakis, PROPER ORTHOGONAL DECOMPOSITION (POD) OF A CLASS OF VIBROIMPACT OSCILLATIONS, Journal of Sound and Vibration, vol.240, issue.5, pp.859-889, 2001.
DOI : 10.1006/jsvi.2000.3264

S. Bellizzi and R. Bouc, A new formulation for the existence and calculation of nonlinear normal modes, Journal of Sound and Vibration, vol.287, issue.3, pp.545-569, 2005.
DOI : 10.1016/j.jsv.2004.11.014
URL : https://hal.archives-ouvertes.fr/hal-00087990

K. S. Breuer and L. Sirovich, The use of the Karhunen-Lo??ve procedure for the calculation of linear eigenfunctions, Journal of Computational Physics, vol.96, issue.2, pp.277-296, 1991.
DOI : 10.1016/0021-9991(91)90237-F

J. Carr, Applications of centre manifold theory, 1981.
DOI : 10.1007/978-1-4612-5929-9

E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede et al., AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), 1998.

C. Elphick, E. Tirapegui, M. Brachet, P. Coullet, and G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica D: Nonlinear Phenomena, vol.29, issue.1-2, pp.95-127, 1987.
DOI : 10.1016/0167-2789(87)90049-2

J. Guckenheimer and P. Holmes, Non-linear oscillations, dynamical systems and bifurcations of vector field, 1983.

G. Iooss and M. Adelmeyer, Topics in bifurcation theory, World Scientific, 1998.

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

D. Jiang, C. Pierre, and S. Shaw, The construction of non-linear normal modes for systems with internal resonance, International Journal of Non-Linear Mechanics, vol.40, issue.5, pp.729-746, 2005.
DOI : 10.1016/j.ijnonlinmec.2004.08.010
URL : https://hal.archives-ouvertes.fr/hal-01350807

D. Jiang, C. Pierre, and S. Shaw, Nonlinear normal modes for vibratory systems under harmonic excitation, Journal of Sound and Vibration, vol.288, issue.4-5, pp.791-812, 2005.
DOI : 10.1016/j.jsv.2005.01.009

G. Kerschen, B. F. Feeny, and J. Golinval, On the exploitation of chaos to build reduced-order models, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.13-14, pp.1785-1795, 2003.
DOI : 10.1016/S0045-7825(03)00206-8

G. Kerschen, J. Golinval, A. F. Vakakis, and L. A. Bergman, The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview, Nonlinear Dynamics, vol.16, issue.417???441, pp.147-169, 2005.
DOI : 10.1007/s11071-005-2803-2

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

W. Lacarbonara, G. Rega, and A. H. Nayfeh, Resonant non-linear normal modes. Part I: analytical treatment for structural one-dimensional systems, International Journal of Non-Linear Mechanics, vol.38, issue.6, pp.851-872, 2003.
DOI : 10.1016/S0020-7462(02)00033-1
URL : https://hal.archives-ouvertes.fr/hal-01403851

Y. V. Mikhlin, Matching of local expansions in the theory of non-linear vibrations, Journal of Sound and Vibration, vol.182, issue.4, pp.577-588, 1995.
DOI : 10.1006/jsvi.1995.0218
URL : https://hal.archives-ouvertes.fr/hal-01347418

F. Pellicano, M. Amabili, and M. P. Païdoussis, Effect of the geometry on the non-linear vibration of circular cylindrical shells, International Journal of Non-Linear Mechanics, vol.37, issue.7, pp.1181-1198, 2002.
DOI : 10.1016/S0020-7462(01)00139-1

E. Pesheck, C. Pierre, and S. 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

H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Gauthiers- Villars, 1892.

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. Sarkar and M. P. Païdoussis, A compact limit-cycle oscillation model of a cantilever conveying fluid, Journal of Fluids and Structures, vol.17, issue.4, pp.525-539, 2003.
DOI : 10.1016/S0889-9746(02)00150-0

A. Sarkar and M. P. Païdoussis, A cantilever conveying fluid: coherent modes versus beam modes, International Journal of Non-Linear Mechanics, vol.39, issue.3, pp.467-481, 2004.
DOI : 10.1016/S0020-7462(02)00213-5

S. Shaw and C. Pierre, Non-linear normal modes and invariant manifolds, Journal of Sound and Vibration, vol.150, issue.1, pp.170-173, 1991.
DOI : 10.1016/0022-460X(91)90412-D
URL : https://hal.archives-ouvertes.fr/hal-01310674

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
URL : http://deepblue.lib.umich.edu/bitstream/2027.42/30744/1/0000394.pdf

L. Sirovich, Turbulence and the dynamics of coherent structures. I. Coherent structures, Quarterly of Applied Mathematics, vol.45, issue.3, pp.561-571, 1987.
DOI : 10.1090/qam/910462

J. C. Slater, A numerical method for determining nonlinear normal modes, Nonlinear Dynamics, vol.27, issue.3, pp.19-30, 1996.
DOI : 10.1007/BF00114796

C. Touzé and M. Amabili, Non-linear normal modes for damped geometrically non-linear systems: application to reduced-order modeling of harmonically forced structures, Journal of Sound and Vibration, 2005.

C. Touzé and O. Thomas, Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry, International Journal of Non-Linear Mechanics, vol.41, issue.5, 2006.
DOI : 10.1016/j.ijnonlinmec.2005.12.004

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, pp.77-101, 2004.
DOI : 10.1016/j.jsv.2003.04.005

A. F. Vakakis, L. I. Manevich, Y. V. Mikhlin, V. N. Philipchuck, and A. A. Zevin, Normal modes and localization in non-linear systems, 1996.

S. Wolfram, The Mathematica Book, 1999.

S. A. Zahorian and M. Rothenberg, Principal component analysis for lowredundancy encoding of speech spectra, Journal of the Acoustical Society of America, vol.69, pp.519-524, 1981.