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

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, R. Pellicano, and M. P. Pa?¨doussispa?¨doussis, 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. Pa?¨doussispa?¨doussis, 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

M. Amabili, F. Pellicano, and A. F. Vakakis, Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results, Journal of Vibration and Acoustics, vol.122, issue.4, pp.346-354, 2000.
DOI : 10.1115/1.1288593

F. Benedettini, G. Rega, and R. Alaggio, Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions, Journal of Sound and Vibration, vol.182, issue.5, pp.775-798, 1995.
DOI : 10.1006/jsvi.1995.0232

A. Chaigne, C. Touzé, and O. Thomas, Mechanical models of musical instruments and sound synthesis: the case of gongs and cymbals, Proceedings of the International Symposium on Musical Acoustics, 2004.

C. Chin and A. H. Nayfeh, A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells, Nonlinear Dynamics, vol.26, issue.1, pp.45-66, 2001.
DOI : 10.1023/A:1012987913909

H. Chu and G. Herrmann, Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, J. Appl. Mech, vol.23, pp.532-540, 1956.

L. H. Donnell, A new theory for the buckling of thin cylinders under axial compression and bending, Trans. Am. Soc. Mech. Eng, vol.56, pp.795-806, 1934.

G. J. Efstathiades, A new approach to the large-deflection vibrations of imperfect circular disks using Galerkin's procedure, Journal of Sound and Vibration, vol.16, issue.2, pp.231-253, 1971.
DOI : 10.1016/0022-460X(71)90485-8

D. A. Evensen, R. E. Fulton, and . Oct, SOME STUDIES ON THE NONLINEAR DYNAMIC RESPONSE OF SHELL-TYPE STRUCTURES, 1965.
DOI : 10.1016/B978-1-4831-9821-7.50018-1

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. 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

P. L. Grossman, B. Koplik, and Y. Yu, Nonlinear Vibrations of Shallow Spherical Shells, Journal of Applied Mechanics, vol.36, issue.3, pp.451-458, 1969.
DOI : 10.1115/1.3564701

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983.

J. Guckenheimer, M. Myers, F. Wicklin, and P. Worfolk, Dstool: a dynamical system toolkit with an interactive graphical interface, 1995.

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

A. Hamdouni and O. Millet, Classification of thin shell models deduced from the nonlinear three-dimensional elasticity, part I: the shallow shells, Arch. Mech, vol.55, issue.2, pp.135-175, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00312225

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

M. W. Johnson and E. Reissner, On transverse vibrations of shallow spherical shells, Quarterly of Applied Mathematics, vol.15, issue.4, pp.367-380, 1956.
DOI : 10.1090/qam/92427

A. Kalnins, Effect of Bending on Vibrations of Spherical Shells, The Journal of the Acoustical Society of America, vol.36, issue.1, pp.74-81, 1964.
DOI : 10.1121/1.1918916

W. T. Koiter, On the nonlinear theory of thin elastic shells, part I, II and III, Proc. Kon. Neth. Akad. Wet, vol.69, pp.1-54, 1965.

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

W. K. Lee, M. H. Yeo, and S. B. Samoilenko, The effect of the number of nodal diameters on non-linear interactions in two asymmetric vibration modes of a circular plate, Journal of Sound and Vibration, vol.268, issue.5, pp.1013-1023, 2003.
DOI : 10.1016/j.jsv.2003.08.006

A. W. Leissa, Vibration of plates, 1969.

A. W. Leissa, Vibration of Shells, Journal of Applied Mechanics, vol.41, issue.2, 1973.
DOI : 10.1115/1.3423343

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. W. Lobitz, A. H. Nayfeh, and D. T. Mook, Non-linear analysis of vibrations of irregular plates, Journal of Sound and Vibration, vol.50, issue.2, pp.203-217, 1977.
DOI : 10.1016/0022-460X(77)90355-8

K. Marguerre, Zur Theorie der Gekrü mmten Platte Grosser Formänderung, Proceedings of the 5th International Congress on Applied Mechanics, pp.93-101, 1938.

J. W. Miles, Resonantly forced motion of two quadratically coupled oscillators, Physica D: Nonlinear Phenomena, vol.13, issue.1-2, pp.247-260, 1984.
DOI : 10.1016/0167-2789(84)90281-1

H. J. Morand and R. Ohayon, Fluid Structure Interaction, 1995.

F. Moussaoui and R. Benamar, NON-LINEAR VIBRATIONS OF SHELL-TYPE STRUCTURES: A REVIEW WITH BIBLIOGRAPHY, Journal of Sound and Vibration, vol.255, issue.1, pp.161-184, 2002.
DOI : 10.1006/jsvi.2001.4146

K. M. Mushtari and K. Z. Galimov, Non-linear theory of thin elastic shells. Israel Program for Scientific Translations, 1957.

A. H. Nayfeh, Nonlinear Interactions: Analytical, Computational, and Experimental Methods, Wiley Series in Nonlinear Science, 2000.
DOI : 10.1115/1.1383674

A. H. Nayfeh and B. Balachandran, Modal Interactions in Dynamical and Structural Systems, Applied Mechanics Reviews, vol.42, issue.11S, pp.175-201, 1989.
DOI : 10.1115/1.3152389

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

A. H. Nayfeh, J. F. Nayfeh, and D. T. Mook, On methods for continuous systems with quadratic and cubic nonlinearities. Nonlinear Dynam, pp.145-162, 1992.

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

A. H. Nayfeh and R. A. Raouf, Non-linear oscillation of circular cylindrical shells, International Journal of Solids and Structures, vol.23, issue.12, pp.1625-1638, 1987.
DOI : 10.1016/0020-7683(87)90113-2

A. H. Nayfeh and L. D. Zavodney, Experimental Observation of Amplitude- and Phase-Modulated Responses of Two Internally Coupled Oscillators to a Harmonic Excitation, Journal of Applied Mechanics, vol.55, issue.3, pp.706-710, 1988.
DOI : 10.1115/1.3125853

F. Pellicano, M. Amabili, and A. F. Vakakis, Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 2: Perturbation Analysis, Journal of Vibration and Acoustics, vol.122, issue.4, pp.355-364, 2000.
DOI : 10.1115/1.1288591

M. S. Qatu, Recent research advances in the dynamic behavior of shells: 1989???2000, Part 2: Homogeneous shells, Applied Mechanics Reviews, vol.55, issue.5, pp.415-434, 1989.
DOI : 10.1115/1.1483078

A. Raman and C. D. Mote-jr, Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed, International Journal of Non-Linear Mechanics, vol.36, issue.2, pp.261-289, 2001.
DOI : 10.1016/S0020-7462(00)00014-7

F. M. Robie, A. A. Popov, and J. Thompson, Auto-parametric resonance in cylindrical shells using geometric averaging, J. Sound Vib, vol.227, issue.1, pp.65-84, 1999.

W. Soedel, Vibration of Plates and Shells, Journal of Vibration Acoustics Stress and Reliability in Design, vol.105, issue.3, 1981.
DOI : 10.1115/1.3269097

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

S. Sridhar, D. T. Mook, and A. H. Nayfeh, Non-linear resonances in the forced responses of plates, part II: Asymmetric responses of circular plates, Journal of Sound and Vibration, vol.59, issue.2, pp.159-170, 1978.
DOI : 10.1016/0022-460X(78)90497-2

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.

W. M. Tien, N. S. Namachchivaya, and A. K. Bajaj, Non-linear dynamics of a shallow arch under periodic excitation ???I.1:2 internal resonance, International Journal of Non-Linear Mechanics, vol.29, issue.3, pp.349-366, 1994.
DOI : 10.1016/0020-7462(94)90007-8

S. A. Tobias and R. N. Arnold, The influence of dynamical imperfection on the vibration of rotating disks, ARCHIVE: Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196), vol.171, issue.1957, pp.669-690, 1957.
DOI : 10.1243/PIME_PROC_1957_171_056_02

C. Touzé and O. Thomas, Reduced-order modeling for a cantilever beam subjected to harmonic forcing. In: proc. of EUROMECH Colloquium 457: nonlinear modes of vibrating systems, pp.165-168, 2004.

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

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

P. Verpeaux, T. Charras, and A. Millard, Calcul des structures et intelligence artificielle, Pluralis Chapter CASTEM CASTEM, 1988.

T. Yamamoto and K. Yasuda, On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System : Forced Vibrations Near the Lower Resonance Point When the Natural Frequencies are in the Ratio 1 : 2, Bulletin of JSME, vol.20, issue.140, pp.168-175, 1977.
DOI : 10.1299/jsme1958.20.168

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

Z. M. Ye, THE NON-LINEAR VIBRATION AND DYNAMIC INSTABILITY OF THIN SHALLOW SHELLS, Journal of Sound and Vibration, vol.202, issue.3, pp.303-311, 1997.
DOI : 10.1006/jsvi.1996.0827

M. H. Yeo and W. K. Lee, CORRECTED SOLVABILITY CONDITIONS FOR NON-LINEAR ASYMMETRIC VIBRATIONS OF A CIRCULAR PLATE, Journal of Sound and Vibration, vol.257, issue.4, pp.653-665, 2002.
DOI : 10.1006/jsvi.2002.5037