N. H. Fletcher, Nonlinear frequency shifts in quasispherical???cap shells: Pitch glide in Chinese gongs, The Journal of the Acoustical Society of America, vol.78, issue.6, pp.2069-2071, 1985.
DOI : 10.1121/1.392664

C. Touzé and A. Chaigne, Lyapunov exponents from experimental time series: application to cymbal vibrations, Acta Acustica, vol.86, issue.3, pp.557-567, 2000.

A. Chaigne, C. Touzé, and O. Thomas, Nonlinear vibrations and chaos in gongs and cymbals, Acoustical Science and Technology, vol.26, issue.5, pp.403-409, 2005.
DOI : 10.1250/ast.26.403
URL : https://hal.archives-ouvertes.fr/hal-01135295

S. A. Tobias, Free undamped non???linear vibrations of imperfect circular disks, Proc. Inst, pp.691-700, 1957.
DOI : 10.1243/PIME_PROC_1957_171_057_02

N. Yamaki, Influence of large amplitudes on flexural vibrations of elastic plates, Zur Angew, Math. Mech, vol.41, issue.12, pp.501-510, 1961.

K. A. Pandalai and M. Sathyamoorthy, On the modal equations of large amplitude flexural vibration of beams, plates, rings and shells, International Journal of Non-Linear Mechanics, vol.8, issue.3, pp.213-218, 1973.
DOI : 10.1016/0020-7462(73)90044-9

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. Touzé, O. Thomas, and A. Chaigne, ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY, Journal of Sound and Vibration, vol.258, issue.4, pp.649-676, 2002.
DOI : 10.1006/jsvi.2002.5143

O. Thomas, C. Touzé, and A. Chaigne, Asymmetric non-linear forced vibrations of free-edge circular plates. Part II: experiments, Journal of Sound and Vibration, vol.265, issue.5, pp.1075-1101, 2003.
DOI : 10.1016/S0022-460X(02)01564-X
URL : https://hal.archives-ouvertes.fr/hal-00830696

G. Prathap and K. A. Pandalai, The role of median surface curvature in large amplitude flexural vibrations of thin shells, Journal of Sound and Vibration, vol.60, issue.1, pp.119-131, 1978.
DOI : 10.1016/0022-460X(78)90405-4

O. Thomas, C. Touzé, and A. Chaigne, Non-linear behavior of gongs through the dynamic of simple rods systems, Proceedings of the International Symposium on Musical Acoustics, pp.173-178, 2001.

H. A. Evensen and R. M. Evan-iwanowsky, Dynamic response and stability of shallow spherical shells subject to time-dependant loading, AIAA J, vol.5, issue.5, pp.969-976, 1967.

P. L. Grossman, B. Koplik, and Y. Yu, Nonlinear Vibrations of Shallow Spherical Shells, Journal of Applied Mechanics, vol.36, issue.3, pp.39-451, 1969.
DOI : 10.1115/1.3564701

K. Yasuda and G. Kushida, Nonlinear Forced Oscillations of a Shallow Spherical Shell, Bulletin of JSME, vol.27, issue.232, pp.2233-2240, 1984.
DOI : 10.1299/jsme1958.27.2233

P. N. Singh, V. Sundarajan, and Y. C. Dias, Large amplitude axisymmetric vibrations of moderately thick spherical caps, Journal of Sound and Vibration, vol.20, issue.3, pp.269-276, 1972.
DOI : 10.1016/0022-460X(72)90607-4

M. Sathyamoorthy, Vibrations of Moderately Thick Shallow Spherical Shells at Large Amplitudes, Journal of Sound and Vibration, vol.172, issue.1, pp.63-70, 1994.
DOI : 10.1006/jsvi.1994.1158

T. K. Varadan and K. A. Pandalai, Nonlinear flexural oscillations of orthotropic shallow spherical shells, Computers & Structures, vol.9, issue.4, pp.417-425, 1978.
DOI : 10.1016/0045-7949(78)90128-1

D. Li, A time-mode approach to nonlinear vibrations of orthotropic thin shallow spherical shells, International Journal of Solids and Structures, vol.30, issue.22, pp.3113-3128, 1993.
DOI : 10.1016/0020-7683(93)90142-T

P. B. Gonçalves, Axisymmetric Vibrations of Imperfect Shallow Spherical Caps Under Pressure Loading, Journal of Sound and Vibration, vol.174, issue.2, pp.249-260, 1994.
DOI : 10.1006/jsvi.1994.1274

D. Hui, Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping, AIAA Journal, vol.21, issue.12, pp.1736-1741, 1983.
DOI : 10.2514/3.8317

A. W. Leissa and A. S. Kadi, Curvature effects on shallow shell vibrations, Journal of Sound and Vibration, vol.16, issue.2, pp.173-187, 1971.
DOI : 10.1016/0022-460X(71)90482-2

D. K. Shin, Large amplitude free vibration behavior of doubly curved shallow open shells with simply-supported edges, Computers & Structures, vol.62, issue.1, pp.35-49, 1997.
DOI : 10.1016/S0045-7949(96)00215-5

K. A. Alhazza, Nonlinear vibrations of doubly-curved cross-ply shallow shells, 19th AIAA Applied Aerodynamics Conference, 2002.
DOI : 10.2514/6.2001-1661

A. H. Nayfeh and W. Lacarbonara, On the discretization of distributedparameter systems with quadratic and cubic non-linearities, Nonlinear Dyn, pp.203-220, 1997.

M. Amabili, Non-linear vibrations of doubly curved shallow shells, International Journal of Non-Linear Mechanics, vol.40, issue.5, pp.683-710, 2005.
DOI : 10.1016/j.ijnonlinmec.2004.08.007

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. 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

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

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. H. Dowell, COMMENTS ON THE NONLINEAR VIBRATIONS OF CYLINDRICAL SHELLS, Journal of Fluids and Structures, vol.12, issue.8, pp.1087-1089, 1998.
DOI : 10.1006/jfls.1998.0183

M. Amabili, F. Pellicano, and M. P. Païdoussis, FURTHER COMMENTS ON NONLINEAR VIBRATIONS OF SHELLS, Journal of Fluids and Structures, vol.13, issue.1, pp.159-160, 1999.
DOI : 10.1006/jfls.1998.0193

D. A. Evensen, NONLINEAR VIBRATIONS OF CYLINDRICAL SHELLS ??? LOGICAL RATIONALE, Journal of Fluids and Structures, vol.13, issue.1, pp.161-164, 1999.
DOI : 10.1006/jfls.1998.0198

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

A. Steindl and H. Troger, Methods for dimension reduction and their application in nonlinear dynamics, International Journal of Solids and Structures, vol.38, issue.10-13, pp.2131-2147, 2001.
DOI : 10.1016/S0020-7683(00)00157-8

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

W. Lacarbonara, A theoretical and experimental investigation of nonlinear vibrations of buckled beams, 1997.

G. Rega, W. Lacarbonara, and A. H. Nayfeh, Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature, Solid Mech, Appl, vol.77, pp.235-246, 2000.

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

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

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.1-2, 2004.
DOI : 10.1016/j.jsv.2003.04.005

O. Thomas, C. Touzé, and A. Chaigne, Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance, International Journal of Solids and Structures, vol.42, issue.11-12, pp.11-12, 2005.
DOI : 10.1016/j.ijsolstr.2004.10.028
URL : https://hal.archives-ouvertes.fr/hal-00830689

O. Thomas, E. Luminais, and C. Touzé, Non-linear modal interactions in freeedge thin spherical shells: measurements of a 1:1:2 internal resonance, Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, 2005.

H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Gauthiers-Villars, p.1892

V. I. Arnold, Chapitres Supplémentaires de la Théorie des Équations Différentielles Ordinaires, Librairie du Globe, 1980.

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

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

C. Touzé, O. Thomas, and A. Huberdeau, Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Computers & Structures, vol.82, issue.31-32, pp.31-32, 2004.
DOI : 10.1016/j.compstruc.2004.09.003

A. H. Nayfeh, D. T. Mook, and N. Oscillations, [49] A. Kalnins, Effect of bending on vibrations of spherical shells, J. Acoust. Soc. Am, vol.36, issue.1, pp.74-81, 1964.