V. Acary and B. Brogliato, Numerical methods for nonsmooth dynamical systems, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

A. Batailly, M. Legrand, A. Millecamps, and F. Garcin, Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact, Journal of Engineering for Gas Turbines and Power, vol.134, issue.8, pp.2012-00746632
DOI : 10.1115/1.4006446
URL : https://hal.archives-ouvertes.fr/hal-00746632

K. Bathe, Finite Element Procedures in Engineering Analysis, Journal of Pressure Vessel Technology, vol.106, issue.4, 1982.
DOI : 10.1115/1.3264375

S. Berberian, Introduction to Hilbert space, 1999.

G. Beylkin, On the Representation of Operators in Bases of Compactly Supported Wavelets, SIAM Journal on Numerical Analysis, vol.29, issue.6, pp.1716-1740, 1992.
DOI : 10.1137/0729097
URL : https://hal.archives-ouvertes.fr/hal-01322928

G. Beylkin and J. Keiser, On the Adaptive Numerical Solution of Nonlinear Partial Differential Equations in Wavelet Bases, Journal of Computational Physics, vol.132, issue.2, pp.233-259, 1997.
DOI : 10.1006/jcph.1996.5562
URL : https://hal.archives-ouvertes.fr/hal-01322927

C. Blatter, Wavelets a primer, 1998.

R. Burgos, M. Silva, and . Santos, Direct solution of differential equations using the wavelet-Galerkin method, Mecanica Computacional, pp.4573-4584, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01333839

S. Burrus, R. Gopinath, and H. Guo, Introduction to wavelets and wavelet transforms: a primer, 1998.

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

M. Chen, C. Hwang, and Y. Shih, THE COMPUTATION OF WAVELET-GALERKIN APPROXIMATION ON A BOUNDED INTERVAL, International Journal for Numerical Methods in Engineering, vol.311, issue.17, pp.2921-2944, 1996.
DOI : 10.1002/(SICI)1097-0207(19960915)39:17<2921::AID-NME983>3.0.CO;2-D
URL : https://hal.archives-ouvertes.fr/hal-01330583

M. Christon and D. Roach, The numerical performance of wavelets for PDEs: the multi-scale finite element, Computational Mechanics, vol.25, issue.2-3, pp.230-244, 2000.
DOI : 10.1007/s004660050472
URL : https://hal.archives-ouvertes.fr/hal-01333698

R. Cook, D. Malkus, M. Plesha, and R. Witt, Concepts and Applications of Finite Element Analysis, 2001.

I. Daubechies, Ten lectures on wavelets, Society for Industrial and Applied Mathematics, 1992.
DOI : 10.1137/1.9781611970104

H. Doi, Fluid/Structure Coupled Aeroelastic Computations for Transonic Flows in Turbomachinery, Volume 4: Turbo Expo 2002, Parts A and B, 2002.
DOI : 10.1115/GT2002-30313
URL : https://hal.archives-ouvertes.fr/hal-01337402

D. Durran, Numerical Methods for Fluid Dynamics With Applications to Geophysics, Texts in Applied Mathematics, 2010.

G. Erlebacher, Y. Hussanini, and L. Jameson, Wavelets: Theory and applications, 1996.

P. Flores, M. Machado, M. Silva, and J. Martins, On the continuous contact force models for soft materials in multibody dynamics, Multibody System Dynamics, vol.24, issue.1, pp.357-375
DOI : 10.1007/s11044-010-9237-4
URL : https://hal.archives-ouvertes.fr/hal-01333699

G. Vongroll and D. Ewins, The harmonic balance method with arc-length continuation in rotor/stator contact problems, International Journal for Numerical Methods in Engineering, vol.241, issue.2, pp.223-233, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01333704
DOI : 10.1006/jsvi.2000.3298

A. Haar, Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, vol.6, issue.3, pp.331-371, 1910.
DOI : 10.1007/BF01456326
URL : https://hal.archives-ouvertes.fr/hal-01333722

M. Holschneider, Wavelet analysis on the circle, Journal of Mathematical Physics, vol.31, issue.1, pp.39-44, 1990.
DOI : 10.1063/1.528825
URL : https://hal.archives-ouvertes.fr/hal-01333726

K. Hunt and E. Crossley, Coefficient of Restitution Interpreted as Damping in Vibroimpact, Journal of Applied Mechanics, vol.42, issue.2, pp.440-445, 1975.
DOI : 10.1115/1.3423596
URL : https://hal.archives-ouvertes.fr/hal-01333795

S. Jiang, Angles between Euclidean subspaces, Geometriae Dedicata, vol.63, issue.2, pp.113-121, 1996.
DOI : 10.1007/BF00148212
URL : https://hal.archives-ouvertes.fr/hal-01333799

L. Lapidus and J. Seinfeld, Numerical solution of ordinary differential equations, 1971.

D. Laxalde and M. Legrand, Nonlinear modal analysis of mechanical systems with frictionless contact interfaces, Computational Mechanics, vol.11, issue.15, pp.469-478, 2011.
DOI : 10.1007/s00466-010-0556-3
URL : https://hal.archives-ouvertes.fr/hal-00413696

M. Legrand, A. Batailly, B. Magnain, C. Cartraud and C. Pierre, Full three-dimensional investigation of structural contact interactions in turbomachines, Journal of Sound and Vibration, vol.331, issue.11, pp.2578-2601, 2012.
DOI : 10.1016/j.jsv.2012.01.017
URL : https://hal.archives-ouvertes.fr/hal-00660863

M. Legrand, S. Roques, C. Pierre, P. Cartraud, and B. Peseux, n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities, Revue Européenne de Mécanique Numérique, pp.269-280, 2006.
DOI : 10.3166/remn.15.269-280
URL : https://hal.archives-ouvertes.fr/hal-00354486

R. Leine and H. Nijmeijer, Dynamics and bifurcations of non-smooth mechanical systems, Lecture Notes in Applied and Computational Mechanics, vol.18, 2006.
DOI : 10.1007/978-3-540-44398-8

X. Li, B. Hu, X. Ling and X. Zeng, A wavelet balance approach for steady-state analysis of nonlinear circuits, 2001 IEEE International Symposium on Circuits and Systems, pp.73-76, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01333733
DOI : 10.1109/TCSI.2002.1001960

G. Liu and S. Quek, The Finite Element Method, 2013.

S. Mallat, A wavelet tour of signal processing. The Sparse Way, 2009.
DOI : 10.1016/B978-0-12-374370-1.X0001-8

Y. Meyer, Ondelettes et opérateurs, 1990.

R. Mickens, Comments on the method of harmonic balance, Journal of Sound and Vibration, vol.94, issue.3, pp.456-460, 1984.
DOI : 10.1016/S0022-460X(84)80025-5
URL : https://hal.archives-ouvertes.fr/hal-01333728

O. Nielsen, Wavelets in Scientific Computing, 1998.
URL : https://hal.archives-ouvertes.fr/tel-00803835

C. Padova, J. Barton, M. Dunn, and S. Manwaring, Experimental Results From Controlled Blade Tip/Shroud Rubs at Engine Speed, Journal of Turbomachinery, vol.129, issue.4, pp.713-723, 2007.
DOI : 10.1115/1.2720869
URL : https://hal.archives-ouvertes.fr/hal-01333702

M. Park, Y.-H. Hwang, Y.-S. Choi and T.-G. Kim, Analysis of a J69-T-25 engine turbine blade fracture, Engineering Failure Analysis, vol.9, issue.5, pp.593-601, 2002.
DOI : 10.1016/S1350-6307(02)00003-1
URL : https://hal.archives-ouvertes.fr/hal-01333729

S. Pernot and C. Lamarque, A WAVELET-GALERKIN PROCEDURE TO INVESTIGATE TIME-PERIODIC SYSTEMS: TRANSIENT VIBRATION AND STABILITY ANALYSIS, Journal of Sound and Vibration, vol.245, issue.5, pp.845-875, 2001.
DOI : 10.1006/jsvi.2001.3610
URL : https://hal.archives-ouvertes.fr/hal-00814563

V. Pilipchuk, Application of special nonsmooth temporal transformations to linear and nonlinear systems under discontinuous and impulsive excitation, Nonlinear Dynamics, vol.18, issue.3, pp.203-234, 1999.
DOI : 10.1023/A:1008331427364
URL : https://hal.archives-ouvertes.fr/hal-01333694

G. Reddien, Projection Methods for Two-Point Boundary Value Problems, SIAM Review, vol.22, issue.2, pp.156-171, 1980.
DOI : 10.1137/1022025
URL : https://hal.archives-ouvertes.fr/hal-01333730

J. Restrepo, G. Mario, and . Leaf, Inner product computations using periodized Daubechies wavelets, International Journal for Numerical Methods in Engineering, vol.24, issue.19, pp.3557-3578, 1997.
DOI : 10.1002/(SICI)1097-0207(19971015)40:19<3557::AID-NME227>3.0.CO;2-A
URL : https://hal.archives-ouvertes.fr/hal-01323007

T. Schindler and V. Acary, Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook, Mathematics and Computers in Simulation, vol.95, pp.180-199
DOI : 10.1016/j.matcom.2012.04.012
URL : https://hal.archives-ouvertes.fr/hal-00762850

L. Shampine and M. Reichelt, The MATLAB ODE Suite, SIAM Journal on Scientific Computing, vol.18, issue.1, pp.1-22, 1997.
DOI : 10.1137/S1064827594276424
URL : https://hal.archives-ouvertes.fr/hal-01333731

G. Strang and T. Nguyen, Wavelets and filter banks, 1996.

A. Strazisar, J. Wood, M. Hathaway, and K. Suder, Laser anemometer measurements in a transoic axial-flow fan rotor, p.11245, 1989.

C. Studer, Numerics of unilateral contacts and friction. Modeling and numerical time integration in non-smooth dynamics, Lecture Notes in Applied and Computational Mechanics, vol.47, 2009.

J. 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

Y. Wang, Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time, Journal of Sound and Vibration, vol.185, issue.1, pp.155-170, 1995.
DOI : 10.1006/jsvi.1994.0369
URL : https://hal.archives-ouvertes.fr/hal-01333696

J. Williams and K. Amaratunga, Introduction to wavelets in engineering, International Journal for Numerical Methods in Engineering, vol.31, issue.14, pp.2365-2388, 1994.
DOI : 10.1002/nme.1620371403
URL : https://hal.archives-ouvertes.fr/hal-01311772

P. Wriggers, Computational Contact Mechanics, 2006.