S. Wei, P. , and C. , Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part II: Forced Vibrations, Journal of Vibration Acoustics Stress and Reliability in Design, vol.110, issue.4, pp.439-449, 1988.
DOI : 10.1115/1.3269548

R. Bladh, M. Castanier, P. , and C. , Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks???Part I: Theoretical Models, Journal of Engineering for Gas Turbines and Power, vol.123, issue.1, pp.89-99, 2001.
DOI : 10.1115/1.1338947

A. Rivas-guerra, M. Mignolet, and J. Delor, Identification of Mistuning Characteristics of Bladed Disks From Free Response Data??? Part II, Journal of Engineering for Gas Turbines and Power, vol.123, issue.2, pp.404-411, 2001.
DOI : 10.1115/1.1338950

M. Mignolet and C. Soize, Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies, Probabilistic Engineering Mechanics, pp.267-278, 2008.
DOI : 10.1016/j.probengmech.2007.12.027
URL : https://hal.archives-ouvertes.fr/hal-00685147

E. Capiez-lernout and C. Soize, Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks, Journal of Engineering for Gas Turbines and Power, vol.126, issue.3, pp.610-618, 2004.
DOI : 10.1115/1.1760527
URL : https://hal.archives-ouvertes.fr/hal-00686199

E. Petrov, Analysis of sensitivity and robustness of forced response for nonlinear dynamic structures, Mechanical Systems and Signal Processing, pp.68-86, 2009.
DOI : 10.1016/j.ymssp.2008.03.008

E. Petrov, Analysis of flutter-induced limit cycle oscillations in gas-turbine structures with friction, gap, and other nonlinear contact interfaces, Journal of Turbomachinery, vol.134, issue.6, 2012.

D. Laxalde, F. Thouverez, J. Sinou, and J. Lombard, Qualitative analysis of forced response of blisks with friction ring dampers, European Journal of Mechanics - A/Solids, vol.26, issue.4, pp.676-687, 2007.
DOI : 10.1016/j.euromechsol.2006.10.002
URL : https://hal.archives-ouvertes.fr/hal-00218249

A. Vakakis, Dynamics of a nonlinear periodic structure with cyclic symmetry, Acta Mechanica, vol.47, issue.10, pp.197-226, 1992.
DOI : 10.1007/BF01170813

E. Sarrouy, A. Grolet, and F. Thouverez, Global and bifurcation analysis of a structure with cyclic symmetry, International Journal of Non-Linear Mechanics, vol.46, issue.5, pp.727-737, 2011.
DOI : 10.1016/j.ijnonlinmec.2011.02.005
URL : https://hal.archives-ouvertes.fr/hal-00746222

A. Grolet and F. Thouverez, Vibration analysis of a nonlinear system with cyclic symmetry, Journal of Engineering for Gas Turbines and Power, vol.133, issue.2, 2011.

A. Grolet and F. Thouverez, Free and forced vibration analysis of a nonlinear system with cyclic symmetry: Application to a simplified model, Journal of Sound and Vibration, vol.331, issue.12, pp.2911-2928, 2012.
DOI : 10.1016/j.jsv.2012.02.008

M. Yang, G. , and J. , A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes, Journal of Engineering for Gas Turbines and Power, vol.123, issue.4, pp.893-900, 2001.
DOI : 10.1115/1.1385197

M. Castanier, P. , and C. , Using Intentional Mistuning in the Design of Turbomachinery Rotors, AIAA Journal, vol.40, issue.10, pp.2077-2086, 2002.
DOI : 10.2514/2.1542

B. Choi, J. Lentz, A. Rivas-guerra, and M. Mignolet, Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment, Journal of Engineering for Gas Turbines and Power, vol.125, issue.1, pp.131-140, 2003.
DOI : 10.1115/1.1498270

M. Mbaye, C. Soize, J. Ousty, and E. Capiez-lernout, Robust analysis of design in vibration of turbomachines, Journal of Turbomachinery, vol.135, issue.2, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00684506

M. Krack, . Panning-von, L. Scheidt, J. Wallaschek, C. Siewert et al., Reduced order modeling based on complex nonlinear modal analysis and its application to bladed disks with shroud contact, Journal of Engineering for Gas Turbines and Power, p.135, 2013.

E. Petrov, A high-accuracy model reduction for analysis of nonlinear vibrations in structures with contact interfaces, Journal of Engineering for Gas Turbines and Power, issue.10, p.133, 2011.

E. Capiez-lernout, C. Soize, and M. Mignolet, nonlinear stochastic dynamics for post-buckling analysis of uncertain cylindrical shells, Proceedings of the International Conference on Recent Advances in Structural Dynamics, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00861281

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, pp.2437-2460, 2013.
DOI : 10.1016/j.jsv.2012.10.017

A. Muryavov, R. , and S. , Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures, Computers & Structures, vol.81, issue.15, pp.1513-1523, 2003.
DOI : 10.1016/S0045-7949(03)00145-7

M. Mignolet and C. Soize, Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.45-48, pp.3951-3963, 2008.
DOI : 10.1016/j.cma.2008.03.032
URL : https://hal.archives-ouvertes.fr/hal-00686140

E. Capiez-lernout, C. Soize, and M. Mignolet, Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity, Computational Mechanics, vol.197, issue.7, pp.87-97, 2012.
DOI : 10.1007/s00466-011-0629-y
URL : https://hal.archives-ouvertes.fr/hal-00684289

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4
URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics, Lecture Notes in Engineering Mechanics 2, 2012.

C. Desceliers and C. Soize, Non-linear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization, International Journal of Non-Linear Mechanics, vol.39, issue.3, pp.343-368, 2004.
DOI : 10.1016/S0020-7462(02)00191-9
URL : https://hal.archives-ouvertes.fr/hal-00686206

P. Davis, Circulant matrices, 1979.

M. Mbaye, C. Soize, and J. Ousty, A reducedorder model of detuned cyclic dynamical systems with geometric modifications using a basis of cyclic modes, ASME Journal of Engineering for Gas Turbines and Power, issue.11, p.132, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684307

D. Thomas, Dynamics of rotationally periodic structures, International Journal for Numerical Methods in Engineering, vol.57, issue.1, pp.81-102, 1979.
DOI : 10.1002/nme.1620140107

A. Bossavit, Boundary Value Problems with Symmetry and Their Approximation by Finite Elements, SIAM Journal on Applied Mathematics, vol.53, issue.5, pp.1352-1380, 1993.
DOI : 10.1137/0153064

C. Soize, Medium frequency linear vibrations of anisotropic elastic structures, La recherche aérospatiale, vol.5, pp.65-87, 1982.
URL : https://hal.archives-ouvertes.fr/hal-00770395

A. W. Bowman and A. Azzalini, Smoothing Techniques for Data Analysis, 1997.