R. M. Rosenberg, On non linear vibrations of systems with many degree of freedom Advances in Applied Mechanics, pp.155-242, 1966.

W. Szemplinska-stupnicka, The Behavior of Nonlinear Vibrating Systems (Volumes I and II), 1990.

L. Jezequel 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

URL : https://hal.archives-ouvertes.fr/hal-00814435

S. W. 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 : https://hal.archives-ouvertes.fr/hal-01544500

E. Pesheck, S. W. Shaw, and C. Pierre, 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

URL : https://hal.archives-ouvertes.fr/hal-01580920

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

S. Bellizzi and R. Bouc, A new formulation for the existence and calculation of nonlinear normal modes, EUROMECH 457 Nonlinear Modes of Vibrating Systems, Press of Ecole Nationale des Travaux Publics de l'Etat, pp.25-28, 2004.
DOI : 10.1016/j.jsv.2004.11.014

URL : https://hal.archives-ouvertes.fr/hal-00087990

S. Bellizzi and R. Bouc, An amplitude-phase formulation for nonlinear modes and limit cycles through invariant manifolds, Journal of Sound and Vibration, vol.300, issue.3-5, 2006.
DOI : 10.1016/j.jsv.2006.09.004

URL : https://hal.archives-ouvertes.fr/hal-00108694

S. Bellizzi and R. Bouc, Nonlinear modes: amplitude-phase formulation and limit cycles analysis, 2nd Int. Conf. on Nonlinear Normal Modes and Localization in Vibrating Systems, 2006.
DOI : 10.1007/1-4020-5370-3_626

URL : https://hal.archives-ouvertes.fr/hal-00097573

J. Hale, Ordinary Differential Equations, 1969.

R. Arquier, F. Pérignon, and B. Cochelin, Numerical Continuation of Non Linear Modes of Elastic Structures, EUROMECH 457 Nonlinear Modes of Vibrating Systems, Press of Ecole Nationale des Travaux Publics de l'Etat, pp.17-20, 2004.

B. Gustafsson, H. O. Kreiss, and J. Oliger, Time dependent problems and difference methods, 1995.
DOI : 10.1002/9781118548448

J. Backus, Small???Vibration Theory of the Clarinet, The Journal of the Acoustical Society of America, vol.35, issue.3, p.1381, 1963.
DOI : 10.1121/1.1918458

J. Kergomard, Mechanics of Musical Instruments (Chap. 6), chapter Elementary considerations on reedinstrument oscillations, 1995.

A. Hirschberg, Mechanics of Musical Instruments (Chap. 7), chapter Aero-acoustics of wind instruments, 1995.

C. J. Nederveen, Acoustical aspects of woodwind instruments, Fritz Knuf pub, 1969.

W. E. Worman, Self-sustained nonlinear oscillations of medium amplitude in clarinet-like systems Ann Arbor University Microfilms (ref, pp.71-22869, 1971.

T. A. Wilson and G. S. Beavers, Operating modes of the clarinet, The Journal of the Acoustical Society of America, vol.56, issue.2, p.653, 1974.
DOI : 10.1121/1.1903304

R. T. Schumacher, calculations of the oscillations of a clarinet, The Journal of the Acoustical Society of America, vol.65, issue.S1, pp.71-85, 1981.
DOI : 10.1121/1.2017413

A. Hirschberg, J. Gilbert, A. P. Wijnands, and A. M. Valkering, Musical aero-acoustics of the clarinet, Le Journal de Physique IV, vol.04, issue.C5, pp.5-559
DOI : 10.1051/jp4:19945120

URL : https://hal.archives-ouvertes.fr/jpa-00252796

V. Debut, Deux études d'un instrument de musique de type clarinette : analyse des fréquences propres du résonateur et calcul des auto-oscillations par décomposition modale, phd (dir, J. Kergomard and F. Laloë

C. Fritz, S. Farner, and J. Kergomard, Some aspects of the harmonic balance method applied to the clarinet, Applied Acoustics, vol.65, issue.12, pp.1155-1180, 2004.
DOI : 10.1016/j.apacoust.2004.04.006

URL : https://hal.archives-ouvertes.fr/hal-00088233