M. Amabili, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers and Structures, vol.82, pp.31-322587, 2004.

M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates, 2008.
DOI : 10.1017/CBO9780511619694

G. Anlas and O. Elbeyli, Nonlinear vibrations of a simply supported rectangular metallic plate subjected to transverse harmonic excitation in the presence of a one-to-one internal resonance, Nonlinear Dynamics, vol.30, issue.1, pp.1-28, 2002.
DOI : 10.1023/A:1020362725706

J. Awrejcewicz, V. A. Krysko, and A. V. Krysko, SPATIO-TEMPORAL CHAOS AND SOLITONS EXHIBITED BY VON K??RM??N MODEL, International Journal of Bifurcation and Chaos, vol.12, issue.07, pp.1465-1513, 2002.
DOI : 10.1142/S021812740200525X

S. Bilbao, A family of conservative finite difference schemes for the dynamical von Karman plate equations, Numerical Methods for Partial Differential Equations, vol.194, issue.1, pp.193-216, 2008.
DOI : 10.1002/num.20260

S. Bilbao, Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics, 2009.
DOI : 10.1002/9780470749012

S. Bilbao, Percussion Synthesis Based on Models of Nonlinear Shell Vibration, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.4, pp.872-880, 2010.
DOI : 10.1109/TASL.2009.2029710

F. Blanc, C. Touzé, J. Mercier, K. Ege, and A. Ben-dhia, On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems, Mechanical Systems and Signal Processing, vol.36, issue.2, p.2012
DOI : 10.1016/j.ymssp.2012.10.016

URL : https://hal.archives-ouvertes.fr/hal-00772317

A. Boudaoud, O. Cadot, B. Odille, and C. Touzé, Observation of Wave Turbulence in Vibrating Plates, Physical Review Letters, vol.100, issue.23, p.234504, 2008.
DOI : 10.1103/PhysRevLett.100.234504

URL : https://hal.archives-ouvertes.fr/hal-00326634

F. Boumediene, L. Duigou, E. H. Boutyour, A. Miloudi, and J. M. Cadou, Nonlinear forced vibration of damped plates by an asymptotic numerical method, Computers & Structures, vol.87, issue.23-24, pp.23-241508, 2009.
DOI : 10.1016/j.compstruc.2009.07.005

URL : https://hal.archives-ouvertes.fr/hal-00494489

A. Chaigne and C. Lambourg, Time-domain simulation of damped impacted plates. I. Theory and experiments, The Journal of the Acoustical Society of America, vol.109, issue.4, pp.1422-1432, 2001.
DOI : 10.1121/1.1354200

URL : https://hal.archives-ouvertes.fr/hal-00830699

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. I. Chang, A. K. Bajaj, and C. M. , Nonlinear oscillations of a fluttering plate, AIAA Journal, vol.4, pp.1267-1275, 1966.

S. I. Chang, A. K. Bajaj, and C. M. , Non-Linear vibrations and chaos in harmonically excited rectangular plates with one-to-one internal resonance, Nonlinear Dynamics, vol.25, issue.5, pp.433-460, 1993.
DOI : 10.1007/BF00053690

W. Q. Chen and H. J. Ding, On free vibration of a functionally graded piezoelectric rectangular plate, Acta Mechanica, vol.32, issue.3-4, pp.207-216, 2002.
DOI : 10.1007/BF01177452

C. Y. Chia, Nonlinear Analysis of Plates, 1980.

H. N. Chu and G. Herrmann, Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, Journal of Applied Mechanics, vol.23, 1956.

O. Doaré and S. Michelin, Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency, Journal of Fluids and Structures, vol.27, issue.8, pp.1357-1375, 2011.
DOI : 10.1016/j.jfluidstructs.2011.04.008

E. Doedel, R. C. Paffenroth, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov et al., Auto2000: Continuation and bifurcation software for ordinary differential equations (with homcont), 2002.

G. Düring, C. Josserand, and S. Rica, Weak Turbulence for a Vibrating Plate: Can One Hear a Kolmogorov Spectrum?, Physical Review Letters, vol.97, issue.2, p.25503, 2006.
DOI : 10.1103/PhysRevLett.97.025503

Y. M. Fu and C. Y. Chia, Nonlinear bending and vibration of symmetrically laminated orthotropic elliptical plate with simply supported edge, Acta Mechanica, vol.62, issue.2, pp.155-170, 1988.
DOI : 10.1007/BF01194348

Y. Gao, B. Xu, and H. Huh, Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields, Acta Mechanica, vol.91, issue.4, pp.99-116, 2010.
DOI : 10.1007/s00707-009-0196-x

M. Géradin and D. Rixen, Mechanical Vibrations, 1997.

R. E. Gordnier and M. R. Visbal, Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter, Fluids 2000 Conference and Exhibit, pp.497-527, 2002.
DOI : 10.2514/6.2000-2337

P. Hagedorn and A. Dasgupta, Vibrations and Waves in Continuous Mechanical Systems, 2007.
DOI : 10.1002/9780470518434

G. Kerschen, M. Peeters, J. C. Golinval, and A. F. Vakakis, Nonlinear normal modes, Part I: A useful framework for the structural dynamicist, Mechanical Systems and Signal Processing, vol.23, issue.1, pp.170-194, 2009.
DOI : 10.1016/j.ymssp.2008.04.002

URL : https://hal.archives-ouvertes.fr/hal-01357931

G. C. Kung and Y. Pao, Nonlinear Flexural Vibrations of a Clamped Circular Plate, Journal of Applied Mechanics, vol.39, issue.4, pp.1050-1054, 1972.
DOI : 10.1115/1.3422827

K. A. Legge and N. H. Fletcher, Nonlinearity, chaos, and the sound of shallow gongs, The Journal of the Acoustical Society of America, vol.86, issue.6, pp.2439-2443, 1989.
DOI : 10.1121/1.398451

A. Leissa, Vibration of plates, 1993.

W. L. Li, Vibration analysis of rectangular plates with general elastic boundary supports, Journal of Sound and Vibration, vol.273, issue.3, pp.619-635, 2003.
DOI : 10.1016/S0022-460X(03)00562-5

A. C. Luo and J. Huang, Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator, Nonlinear Dynamics, vol.22, issue.2, pp.417-438, 2013.
DOI : 10.1007/s11071-012-0725-3

J. C. Golinval, C. Stephan, P. Lubrina, M. Peeters, and G. Kerschen, Nonlinear normal modes of a full-scale aircraft, 29th International Modal Analysis Conference, 2011.

J. Meenen and H. Altenbach, A consistent deduction of von K???rm???n-type plate theories from three-dimensional nonlinear continuum mechanics, Acta Mechanica, vol.37, issue.1, pp.1-17, 2001.
DOI : 10.1007/BF01182348

N. Mordant, Are There Waves in Elastic Wave Turbulence?, Physical Review Letters, vol.100, issue.23, p.234505, 2008.
DOI : 10.1103/PhysRevLett.100.234505

URL : https://hal.archives-ouvertes.fr/hal-00712175

N. Mordant, Fourier analysis of wave turbulence in a thin elastic plate, The European Physical Journal B, vol.2, issue.4, pp.537-545, 2010.
DOI : 10.1140/epjb/e2010-00197-y

URL : https://hal.archives-ouvertes.fr/hal-00712159

M. O. Moussa, Z. Moumni, O. Doaré, C. Touzé, and W. Zaki, Non-linear dynamic thermomechanical behaviour of shape memory alloys, Journal of Intelligent Material Systems and Structures, vol.23, issue.14, pp.1593-1611, 2012.
DOI : 10.1177/1045389X12448446

URL : https://hal.archives-ouvertes.fr/hal-00838865

K. D. Murphy, L. N. Virgin, and S. A. Rizzi, CHARACTERIZING THE DYNAMIC RESPONSE OF A THERMALLY LOADED, ACOUSTICALLY EXCITED PLATE, Journal of Sound and Vibration, vol.196, issue.5, pp.635-658, 1996.
DOI : 10.1006/jsvi.1996.0506

A. H. Nayfeh, Nonlinear Oscillations, 1995.

A. H. Nayfeh and P. F. Pai, Linear and Nonlinear Structural Mechanics, 2004.
DOI : 10.1002/9783527617562

U. Parlitz and W. Lauterborn, Superstructure in the bifurcation set of the Duffing equation, Physics Letters A, vol.107, issue.8, pp.351-355, 1985.
DOI : 10.1016/0375-9601(85)90687-5

M. Peeters, R. Viguié, G. Sérandour, G. Kerschen, and J. Golinval, Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques, Mechanical Systems and Signal Processing, vol.23, issue.1, pp.195-216, 2009.
DOI : 10.1016/j.ymssp.2008.04.003

P. Ribeiro, Nonlinear vibrations of simply-supported plates by the p-version finite element method. Finite Elements in Analysis and Design, pp.9-10911, 2005.

P. Ribeiro and M. Petyt, GEOMETRICAL NON-LINEAR, STEADY STATE, FORCED, PERIODIC VIBRATION OF PLATES, PART I: MODEL AND CONVERGENCE STUDIES, Journal of Sound and Vibration, vol.226, issue.5, pp.955-983, 1999.
DOI : 10.1006/jsvi.1999.2306

P. Ribeiro and M. Petyt, GEOMETRICAL NON-LINEAR, STEADY STATE, FORCED, PERIODIC VIBRATION OF PLATES, PART II: STABILITY STUDY AND ANALYSIS OF MULTI-MODAL RESPONSE, Journal of Sound and Vibration, vol.226, issue.5, pp.985-1010, 1999.
DOI : 10.1006/jsvi.1999.2336

M. Sathyamoorthy, Nonlinear Vibrations of Plates: An Update of Recent Research Developments, Applied Mechanics Reviews, vol.49, issue.10S, pp.55-62, 1996.
DOI : 10.1115/1.3101977

O. Thomas and S. Bilbao, Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties, Journal of Sound and Vibration, vol.315, issue.3, pp.569-590, 2008.
DOI : 10.1016/j.jsv.2008.04.014

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.423339-3373, 1112.
DOI : 10.1016/j.ijsolstr.2004.10.028

URL : https://hal.archives-ouvertes.fr/hal-00830689

C. Touzé, S. Bilbao, and O. Cadot, Transition scenario to turbulence in thin vibrating plates, Journal of Sound and Vibration, vol.331, issue.2, pp.412-433, 2011.
DOI : 10.1016/j.jsv.2011.09.016

C. Touzé, O. Thomas, and M. Amabili, Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates, International Journal of Non-Linear Mechanics, vol.46, issue.1, pp.234-246, 2011.
DOI : 10.1016/j.ijnonlinmec.2010.09.004

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

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.2671-2682, 2004.
DOI : 10.1016/j.compstruc.2004.09.003

A. F. Vakakis, NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW, Mechanical Systems and Signal Processing, vol.11, issue.1, pp.3-22, 1997.
DOI : 10.1006/mssp.1996.9999

URL : https://hal.archives-ouvertes.fr/hal-01354037

T. Von-kármán, Festigkeitsprobleme im maschinenbau, Encyklopadie der Mathematischen Wissenschaften, pp.311-385, 1910.

N. Yamaki, Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates, Zeitschrift für Angewandte Mathematik und Mechanik, pp.501-510, 1961.
DOI : 10.1002/zamm.19610411204

X. L. Yang and P. R. Sethna, Local and global bifurcations in parametrically excited vibrations of nearly square plates, International Journal of Non-Linear Mechanics, vol.26, issue.2, pp.199-220, 1991.
DOI : 10.1016/0020-7462(91)90052-U