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. Pa?¨doussispa?¨doussis, 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. Pa?¨doussispa?¨doussis, 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. Pa?¨doussispa?¨doussis, 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

D. A. Evensen, Nonlinear flexural vibrations of thin-walled circular cylinders, 1967.

I. T. Georgiou, Advanced Proper Orthogonal Decomposition Tools: Using Reduced Order Models to Identify Normal Modes of Vibration and Slow Invariant Manifolds in the Dynamics of Planar Nonlinear Rods, Nonlinear Dynamics, vol.50, issue.9, pp.69-110, 2005.
DOI : 10.1007/s11071-005-2793-0

I. T. Georgiou, I. Schwartz, E. Emaci, and A. Vakakis, Interaction Between Slow and Fast Oscillations in an Infinite Degree-of-Freedom Linear System Coupled to a Nonlinear Subsystem: Theory and Experiment, Journal of Applied Mechanics, vol.66, issue.2, pp.448-459, 1999.
DOI : 10.1115/1.2791069

J. Guckenheimer and P. Holmes, Non-linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983.

L. Je´ze´quelje´ze´je´ze´quel 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. Pa?¨doussispa?¨doussis, 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

P. Poincare´ and H. , Les me´thodesme´thodes nouvelles de la me´caniqueme´canique ceíeste. 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. Pa?¨doussispa?¨doussis, 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. Pa?¨doussispa?¨doussis, 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

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

T. Touze´, C. Amabili, and M. , Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures, Journal of Sound and Vibration, vol.298, issue.4-5, pp.958-981, 2006.
DOI : 10.1016/j.jsv.2006.06.032
URL : https://hal.archives-ouvertes.fr/hal-00838883

T. Touze´, C. Thomas, and O. , Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry, International Journal of Non-Linear Mechanics, vol.41, issue.5, pp.678-692, 2006.
DOI : 10.1016/j.ijnonlinmec.2005.12.004
URL : https://hal.archives-ouvertes.fr/hal-00838885

T. Touze´, C. Thomas, O. Chaigne, and A. , 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
URL : https://hal.archives-ouvertes.fr/hal-00830693

A. F. Vakakis, L. I. Manevich, Y. V. Mikhlin, V. N. Pilipchuk, and A. A. Zevin, Normal Modes and Localization in Non-Linear Systems, 1996.

S. Wolfram, The Mathematica Book, fourth ed, 1999.

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