C. Pierre, A. Ferri, and E. Dowell, Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method, Journal of Applied Mechanics, vol.52, issue.4, pp.958-964, 1985.
DOI : 10.1115/1.3169175

S. Lau, Y. Cheung, and S. Wu, Incremental Harmonic Balance Method With Multiple Time Scales for Aperiodic Vibration of Nonlinear Systems, Journal of Applied Mechanics, vol.50, issue.4a, pp.871-876, 1983.
DOI : 10.1115/1.3167160

J. H. Wang and W. K. Chen, Investigation of the Vibration of a Blade With Friction Damper by HBM, Journal of Engineering for Gas Turbines and Power, vol.115, issue.2, pp.294-299, 1993.
DOI : 10.1115/1.2906708

URL : https://hal.archives-ouvertes.fr/hal-01333736

T. Cameron and J. Griffin, An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems, Journal of Applied Mechanics, vol.56, issue.1, pp.149-154, 1989.
DOI : 10.1115/1.3176036

URL : https://hal.archives-ouvertes.fr/hal-01333697

J. Guillen and C. Pierre, An Efficient, Hybrid, Frequency-Time Domain Method for The Dynamics of Large-Scale Dry-Friction Damped Structural Systems., IUTAM Symposium on Unilateral Multibody Contact, 1999.
DOI : 10.1007/978-94-011-4275-5_17

O. Poudou, Modeling of friction damping in bladed disk assemblies, 1999.

B. S. Garbow, K. E. Hillstrom, and J. J. More, User Guide for Minpack-1, 1980.

M. J. Powell, A hybrid method for nonlinear equations, Numerical Methods for Nonlinear Equations, 1969.

J. H. Griffin, Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils, Journal of Engineering for Power, vol.102, issue.2, pp.329-333, 1980.
DOI : 10.1115/1.3230256

W. E. Whiteman and A. A. Ferri, Analysis of beam-like structures with displacement-dependent friction forces: Part I: single-degree-of-freedom model, Proc. of ASME 1995 Design Engineering Technical Conferences, Symp. on Friction Damping and Friction-Induced Vibration, pp.1093-1100, 1995.

W. E. Whiteman and A. A. Ferri, Analysis of beam-like structures with displacement-dependent friction forces: Part II: multi-degree-of-freedom model, Proc. of ASME 1995 Design Engineering Technical Conferences, Symp. on Friction Damping and Friction-Induced Vibration, pp.1101-1108, 1995.

K. Y. Sanliturk, M. Imregun, and D. J. Ewins, Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers, Journal of Vibration and Acoustics, vol.119, issue.1, pp.96-103, 1997.
DOI : 10.1115/1.2889693

A. A. Ferri and B. S. Heck, Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory, Journal of Vibration and Acoustics, vol.120, issue.2, pp.588-595, 1998.
DOI : 10.1115/1.2893868

C. H. Menq, J. H. Griffin, and J. Bielak, The Influence of a Variable Normal Load on the Forced Vibration of a Frictionally Damped Structure, Journal of Engineering for Gas Turbines and Power, vol.108, issue.2, pp.300-305, 1986.
DOI : 10.1115/1.3239903

B. D. Yang, M. L. Chu, and C. H. Menq, STICK???SLIP???SEPARATION ANALYSIS AND NON-LINEAR STIFFNESS AND DAMPING CHARACTERIZATION OF FRICTION CONTACTS HAVING VARIABLE NORMAL LOAD, Journal of Sound and Vibration, vol.210, issue.4, pp.410-481, 1998.
DOI : 10.1006/jsvi.1997.1305

C. H. Menq and B. D. Yang, NON-LINEAR SPRING RESISTANCE AND FRICTION DAMPING OF FRICTIONAL CONSTRAINT HAVING TWO-DIMENSIONAL MOTION, Journal of Sound and Vibration, vol.217, issue.1, pp.149-154, 1989.
DOI : 10.1006/jsvi.1998.1739

C. H. Menq, P. Chidamparam, and J. H. Griffin, Friction damping of two-dimensional motion and its application in vibration control, Journal of Sound and Vibration, vol.144, issue.3, pp.427-447, 1991.
DOI : 10.1016/0022-460X(91)90562-X

K. Y. Sanliturk and D. J. Ewins, MODELLING TWO-DIMENSIONAL FRICTION CONTACT AND ITS APPLICATION USING HARMONIC BALANCE METHOD, Journal of Sound and Vibration, vol.193, issue.2, pp.511-523, 1996.
DOI : 10.1006/jsvi.1996.0299

B. D. Yang and J. H. Griffin, CHARACTERIZATION OF 3D CONTACT KINEMATICS AND PREDICTION OF RESONANT RESPONSE OF STRUCTURES HAVING 3D FRICTIONAL CONSTRAINT, Journal of Sound and Vibration, vol.217, issue.5, pp.909-925, 1998.
DOI : 10.1006/jsvi.1998.1802

B. D. Yang and C. H. Menq, Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 1???Stick-Slip Contact Kinematics, Journal of Engineering for Gas Turbines and Power, vol.120, issue.2, pp.410-417, 1998.
DOI : 10.1115/1.2818138

B. D. Yang and C. H. Menq, Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 2???Prediction of Forced Response and Experimental Verification, Journal of Engineering for Gas Turbines and Power, vol.120, issue.2, pp.418-423, 1998.
DOI : 10.1115/1.2818139

C. H. Menq, J. Bielak, and J. H. Griffin, The influence of microslip on vibratory response, part I: A new microslip model, Journal of Sound and Vibration, vol.107, issue.2, pp.279-293, 1986.
DOI : 10.1016/0022-460X(86)90238-5

C. H. Menq, J. H. Griffin, and J. Bielak, The influence of microslip on vibratory response, Part II: A comparison with experimental results, Journal of Sound and Vibration, vol.107, issue.2, pp.295-307, 1986.
DOI : 10.1016/0022-460X(86)90239-7

G. Csaba, Friction damping of turbine blade vibrations using a microslip model, Journal of Machine Vibration, vol.4, pp.2-7, 1995.

E. J. Berger, M. R. Begley, and M. Mahajani, Structural Dynamic Effects on Interface Response: Formulation and Simulation Under Partial Slipping Conditions, Journal of Applied Mechanics, vol.67, issue.4, pp.785-792, 2000.
DOI : 10.1115/1.1330545

T. A. Laursen and J. C. Simo, A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems, International Journal for Numerical Methods in Engineering, vol.44, issue.20, pp.3451-3485, 1993.
DOI : 10.1137/1.9781611970845

J. Heegaard and A. Curnier, An augmented Lagrangian method for discrete large-slip contact problems, International Journal for Numerical Methods in Engineering, vol.19, issue.4, pp.569-593, 1993.
DOI : 10.1137/1.9781611970838

P. Wriggers and G. Zavarise, Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces, Communications in Numerical Methods in Engineering, vol.94, issue.10, pp.815-824, 1993.
DOI : 10.1016/0045-7825(92)90061-N

T. A. Laursen and B. N. , An augmented Lagrangian quasi-Newton solver for constrained nonlinear finite element applications, International Journal for Numerical Methods in Engineering, vol.85, issue.21, pp.3571-3590, 1995.
DOI : 10.1137/1.9781611970845

R. Craig and M. Bampton, Coupling of substructures for dynamic analysis, American Institute of Aeronautics and Astronautics Journal, vol.8, issue.7, pp.1313-1319, 1968.

M. Berthillier, C. Dupont, R. Mondal, and J. J. Barrau, Bladed forced response analysis with friction dampers, Journal of Engineering for Gas Turbines and Power, vol.120, pp.468-474, 1998.
DOI : 10.1115/1.2893853