S. Wei and C. Pierre, 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, and C. Pierre, 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

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

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. Castanier and C. Pierre, 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, R. A. , 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

Y. Chan and D. Ewins, Management of the variability of vibration response levels in mistuned bladed discs using robust design concept. part 1: Parameter design, Mechanical Systems and Signal Processing, pp.2777-2791, 2010.

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, pp.21008-21009, 2013.
DOI : 10.1115/1.4007442
URL : https://hal.archives-ouvertes.fr/hal-00684506

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

E. Petrov, Analysis of sensitivity and robustness of forced response for nonlinear dynamic structures, Mechanical Systems and Signal Processing, vol.23, issue.1, 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, pp.61018-61019, 2012.
DOI : 10.1115/1.4006292

A. Muryavov and S. Rizzi, 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

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, pp.22502-22503, 2011.
DOI : 10.1115/1.4001989

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

L. Sirovich, Turbulence and the dynamics of coherent structures. I. Coherent structures, Quarterly of Applied Mathematics, vol.45, issue.3, pp.561-571, 1987.
DOI : 10.1090/qam/910462

E. Capiez-lernout, C. Soize, and M. Mignolet, Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.271, pp.210-230, 2014.
DOI : 10.1016/j.cma.2013.12.011
URL : https://hal.archives-ouvertes.fr/hal-00922708

M. Mignolet, A. Przekop, S. Rizzi, and S. 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

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. Touze, M. Vidrascu, and D. Chapelle, Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models, Computational Mechanics, vol.298, issue.4???5, pp.567-580, 2014.
DOI : 10.1007/s00466-014-1006-4
URL : https://hal.archives-ouvertes.fr/hal-00955582

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics, Lecture Notes in Engineering Mechanics, vol.2, p.2012
DOI : 10.1061/9780784412237
URL : https://hal.archives-ouvertes.fr/hal-00749201

C. Desceliers, C. Soize, and S. Cambier, Non-parametric???parametric model for random uncertainties in non-linear structural dynamics: application to earthquake engineering, Earthquake Engineering & Structural Dynamics, vol.33, issue.3, pp.315-327, 2003.
DOI : 10.1002/eqe.352
URL : https://hal.archives-ouvertes.fr/hal-00686208

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

L. Wagner and J. Griffin, A Continuous Analog Model for Grouped-Blade Vibration, Journal of Sound and Vibration, vol.165, issue.3, pp.421-438, 1993.
DOI : 10.1006/jsvi.1993.1268

J. Kenyon, J. Griffin, and N. Kim, Sensitivity of Tuned Bladed Disk Response to Frequency Veering, Journal of Engineering for Gas Turbines and Power, vol.127, issue.4, pp.835-842, 2005.
DOI : 10.1115/1.1924486

P. Bisegna and G. Caruso, Dynamical behavior of disordered rotationally periodic structures: A homogenization approach, Journal of Sound and Vibration, vol.330, issue.11, pp.2608-2627, 2011.
DOI : 10.1016/j.jsv.2010.12.009

Y. Chan and D. Ewins, The Amplification of Vibration Response Levels of Mistuned Bladed Disks: Its Consequences and Its Distribution in Specific Situations, Journal of Engineering for Gas Turbines and Power, vol.133, issue.10, pp.102502-102503, 2011.
DOI : 10.1115/1.4003021

R. De-borst, M. Crisfield, J. Remmers, and C. Verhoosel, Non-linear finite element analysis of solids and structures, 2012.
DOI : 10.1002/9781118375938