R. J. Allemang and D. L. Brown, Experimental modal analysis, Shock 655 and vibration handbook, 2009.

J. Noël and G. Kerschen, Nonlinear system identication in structural dynamics: 10 more years of progress, Mechanical Systems and Signal Processing, vol.83, issue.235, 2016.

G. Kerschen, K. Worden, A. F. Vakakis, and J. Golinval, Past, present and future of nonlinear system identication in structural dynamics, Mechanical Systems and Signal Processing, vol.20, issue.505592, p.660, 2006.

K. Worden and G. R. Tomlinson, Nonlinearity in structural synamics. Detection, identication and modelling, 2001.

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

A. Lazarus, O. Thomas, and J. F. Deü, Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS, Finite Elements in Analysis and Design, vol.49, issue.1, pp.665-3551, 2012.
DOI : 10.1016/j.finel.2011.08.019

URL : https://hal.archives-ouvertes.fr/hal-01084700

O. Thomas, B. Legrand, and C. , Optimization of Length and Thickness of Smart Transduction Layers on Beam Structures for Control and M/NEMS Applications, Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems, pp.2015-8857
DOI : 10.1115/SMASIS2015-8857

URL : https://hal.archives-ouvertes.fr/hal-01203144

M. K. Samal, P. Seshu, S. Parashar, U. V. Wagner, P. Hagedorn et al., A nite element model for nonlinear behaviour of piezoceramics under weak electric elds, Finite Elements in Analysis and Design, pp.41-14641480, 2005.

L. Jezequel and C. Lamarque, Analysis of non-linear dynamical systems by the normal form theory Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes, Journal of Sound and Vibration Journal of Sound and Vibration, vol.149, issue.77101, pp.1-2, 1991.

C. Touzé and O. Thomas, Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry, International Journal of Non-Linear Mechanics, vol.41, issue.5, 2006.
DOI : 10.1016/j.ijnonlinmec.2005.12.004

M. Amabili, ]. O. Thomas, C. Touzé, and A. Chaigne, Nonlinear Vibrations and Stability of Shells and Plates 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.3339, pp.68011-68023, 2005.

C. Touzé, C. Camier, G. Favraud, and O. Thomas, Eect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells, Mathematical Problems in Engineering, p.685, 2008.

O. Thomas, F. Mathieu, W. Manseld, C. Huang, S. Trolier-mckinstry et al., Efficient parametric amplification in micro-resonators with integrated piezoelectric actuation and sensing capabilities, Applied Physics Letters, vol.102, issue.16, p.163504, 2013.
DOI : 10.1063/1.2338139

N. Kacem, J. Arcamone, F. Perez-murano, and S. Hentz, Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications, Journal of Micromechanics and Microengineering, vol.20, issue.4, p.45023, 2010.
DOI : 10.1088/0960-1317/20/4/045023

M. K. Samal, P. Seshu, S. Parashar, U. Von-wagner, P. Hagedorn et al., A nite element model for nonlinear behaviour of piezoceramics under weak electric elds, Finite Elements in Analysis and Design. 695 [18] S. Mojrzisch, J. Twiefel, Phase-controlled frequency response measurement of a piezoelectric ring at high vibration amplitude, Archive of Applied Mechanics, vol.86, issue.10, p.17631769, 2015.

S. Peter and R. I. Leine, Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation, Mechanical Systems and Signal Processing, vol.96, p.139158, 2017.
DOI : 10.1016/j.ymssp.2017.04.011

O. Thomas, C. Touzé, and A. Chaigne, Asymmetric non-linear forced vibrations of free-edge circular plates, p.700
URL : https://hal.archives-ouvertes.fr/hal-00830696

M. P. Mignolet, A. Przekop, S. A. Rizzi, and S. M. Spottswood, A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures, Journal of Sound and Vibration, vol.332, issue.10, p.24372460, 2013.
DOI : 10.1016/j.jsv.2012.10.017

C. Touzé, M. Vidrascu, and D. Chapelle, Direct nite element computation of non-linear modal coupling coecients for reduced-order shell models, Computational Mechanics, vol.54, issue.567580, 2014.

M. Géradin and D. Rixen, Mechanical Vibrations: Theory and Applications to Structural Dynamics, J. Wiley & Sons, 2015.

A. A. Muravyov and S. A. Rizzi, Determination of nonlinear stiness with application to random vibration of 710 geometrically nonlinear structures, Computers and Structures, vol.81, issue.15, p.15131523, 2003.

O. Thomas and S. Bilbao, Geometrically nonlinear exural vibrations of plates: In-plane boundary conditions and some symmetry properties, Journal of Sound and Vibration, vol.315, issue.3, p.569590, 2008.

C. Camier, C. Touzé, and O. Thomas, Non-linear vibrations of imperfect free-edge circular plates and shells, European Journal of Mechanics A Amabili, Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures, Journal of Sound and Vibration, vol.28, issue.298, pp.7154-7159, 2006.

G. Kerschen, M. Peeters, J. C. Golinval, and A. F. Vakakis, Nonlinear normal modes, Part I: A useful framework for the structural dynamicist Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Mechanical Systems and Signal Processing Computers and Structures, vol.23, issue.82, pp.31-32, 2004.

C. Touzé, M. Amabili, and O. Thomas, Reduced-order models for large-amplitude vibrations of shells including in-plane inertia, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.21-24, pp.21-24, 2008.
DOI : 10.1016/j.cma.2008.01.002

S. W. Shaw and C. Pierre, Nonlinear normal modes and invariant manifolds, Journal of Sound and Vibration, vol.725, issue.1, pp.150-170173, 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 of Vibration for Non-Linear Continuous Systems, Journal of Sound and Vibration, vol.169, issue.3, p.319347, 1994.
DOI : 10.1006/jsvi.1994.1021

URL : https://hal.archives-ouvertes.fr/hal-01471098

R. M. Rosenberg, On non-linear vibrations of systems with many degrees of freedom, Problème général de la stabilité du mouvement, Annales de la faculté des sciences de Toulouse, 1966.

A. F. Kelley, Analytic two-dimensional subcenter manifolds for systems with an integral, Pacific Journal of Mathematics, vol.29, issue.2, 1969.
DOI : 10.2140/pjm.1969.29.335

G. Haller and S. Ponsioen, Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction, Nonlinear Dynamics, vol.57, issue.2, p.14931534, 2016.
DOI : 10.1137/130933058

O. Thomas, C. Touzé, and E. Luminais, Modèles réduits de structures minces en vibrations non-linéaires, Colloque national en calcul de structure, p.16, 2005.

M. Monteil, O. Thomas, and C. Touzé, Identication of mode couplings in nonlinear vibrations of the steelpan, Thomas, C. Vergez, MANLAB 2.0, an interactive continuation software, p.740, 2010.

J. R. Wright, J. E. Cooper, and M. J. Desforges, Normal-mode force appropriation -theory and application, Mechanical Syatems and Signal Processing, Dynamic testing of nonlinear vibrating structures using nonlinear normal modes, 1999.

S. Baguet and B. Cochelin, Determination of branches of limit points by an asymptotic numerical method Hardening / softening behaviour of antiresonance for nonlinear torsional vibration absorbers, European Congress on Computational Methods in Applied Sciences and Engineering Proc. of the 24th. International Congress on Theoretical and Applied Mechanics, pp.1114-750, 2000.

O. Thomas, C. Touzé, A. Chaigne, M. Peeters, G. Kerschen et al., Non-linear behaviour of gongs through the dynamics of simple rods systems, in: Proceedings of ISMA, Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration, Mechanical Systems and Signal Processing, pp.755-801, 2001.

J. M. Londoño, S. A. Neild, and J. E. Cooper, Identication of backbone curves of nonlinear systems from resonance decay responses Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay, Mechanical Systems and Signal Processing, pp.76-77, 2015.

S. Peter, R. Riethmüller, R. I. Leine, I. J. Sokolov, and V. I. Babitsky, Tracking of backbone curves of nonlinear systems using phase-lockedloops , in: Conference Proceedings of the Society for Phase control of self-sustained vibration, Experimental Mechanics Series Journal of Sound and Vibration, vol.1, issue.2484, p.725744, 2001.

S. Mojrzisch, J. Wallaschek, and J. Bremer, An Experimental Method for the Phase Controlled Frequency Response Measurement of Nonlinear Vibration Systems, PAMM, vol.12, issue.1, p.253254, 2012.
DOI : 10.1002/pamm.201210117

J. Sieber and B. Krauskopf, Control based bifurcation analysis for experiments, Nonlinear Dynamics, vol.74, issue.1, 2008.
DOI : 10.1007/978-1-4757-3978-7

URL : http://dare.ubvu.vu.nl/bitstream/1871/27269/1/224261.pdf

E. Bureau, F. Schilder, M. Elmegård, I. F. Santos, J. J. Thomsen et al., Experimental bifurcation analysis of an impact oscillator???Determining stability, Journal of Sound and Vibration, vol.333, issue.21, 2014.
DOI : 10.1016/j.jsv.2014.05.032

L. Renson, A. Gonzalez-buelga, D. A. Barton, and S. A. Neild, Robust identication of backbone curves 775 using control-based continuation, Journal of Sound and Vibration, vol.367, p.145158, 2016.

D. A. Barton, Control-based continuation: Bifurcation and stability analysis for physical experiments, Mechanical Systems and Signal Processing, vol.84, issue.5464, 2017.
DOI : 10.1016/j.ymssp.2015.12.039

O. Thomas, C. Touzé, and . Luminais, Non-linear vibrations of free-edge thin spherical shells: Experiments on a 1:1:2 internal resonance Digital signal processing for an adaptive phaselocked loop controller, Nonlinear Dynamics Proceedings of SPIE, vol.49, issue.6926, pp.780-69260, 2007.

M. Fan, M. Clark, and Z. C. Feng, Implementation and stability study of phase-locked-loop nonlinear dynamic measurement systems, Communications in Nonlinear Science and Numerical Simulation, vol.12, issue.7, p.1302, 2007.
DOI : 10.1016/j.cnsns.2006.01.018

J. A. Sanders, F. Verhulst, and J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, 2007.
DOI : 10.1007/978-1-4757-4575-7

C. Touzé, O. Thomas, and A. Chaigne, Asymmetric non-linear forced vibrations of free-edge circular plates, p.790

P. S. Varoto and L. P. De-oliveira, On the Force Drop Off Phenomenon in Shaker Testing in Experimental Modal Analysis, Shock and Vibration, vol.9, issue.4-5, p.165175, 2002.
DOI : 10.1155/2002/675674

A. I. Manevitch and L. I. Manevitch, Free oscillations in conservative and dissipative symmetric cubic twodegree-of-freedom systems with closed natural frequencies Fletcher, Nonlinear frequency shifts in quasispherical-cap shells: Pitch glide in Chinese gongs, Journal of the Acoustical Society of America, vol.3864, issue.786, p.795, 1985.

T. D. Rossing and N. H. Fletcher, Nonlinear vibrations in plates and gong, The Journal of the Acoustical Society of America, vol.73, p.345351, 1983.

S. R. Anton and H. A. Sodano, A review of power harvesting using piezoelectric materials, Smart Materials 800 and Structures, pp.1-21, 2007.

M. F. Daqaq, R. Masana, A. Erturk, and D. D. Quinn, On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion, Applied Mechanics Reviews, vol.66, issue.4, p.40801, 2014.
DOI : 10.1115/1.4026278

J. Ducarne, O. Thomas, and J. F. Deü, Placement and dimension optimization of shunted piezoelectric patches for vibration reduction Non-linear non-planar oscillations of a cantilever beam under lateral base excitations, 2012) 32863303. 805, p.455474, 1990.