J. Bonet and R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, 2008.
DOI : 10.1017/CBO9780511755446

I. K. Chatjigeorgiou, Numerical simulation of the chaotic lateral vibrations of long rotating beams, Applied Mathematics and Computation, vol.219, issue.10, pp.5592-5612
DOI : 10.1016/j.amc.2012.11.076

A. Chevallier, Nonlinear Stochastic Drilling Vibrations, 2000.

C. Jr and A. , Modeling and Uncertainty Quantification in the Nonlinear Stochastic Dynamics of a Horizontal Dsrillstrings, 2015.

A. Depouhon and E. Detournay, Instability regimes and self-excited vibrations in deep drilling systems, Journal of Sound and Vibration, vol.333, issue.7, pp.2019-2039
DOI : 10.1016/j.jsv.2013.10.005

Y. Hu, Q. Di, W. Zhu, Z. Chen, and W. W. , Dynamic characteristics analysis of drillstring in the ultra-deep well with spatial curved beam finite element, Journal of Petroleum Science and Engineering, vol.82, issue.83, pp.166-173
DOI : 10.1016/j.petrol.2012.01.011

T. J. Hughes, The Finite Element Method, 2000.

K. H. Hunt and F. 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

Y. A. Khulief and F. A. Al-sulaiman, Vibration analysis of drillstrings with self-excited stick???slip oscillations, Journal of Sound and Vibration, vol.299, issue.3, pp.540-558, 2007.
DOI : 10.1016/j.jsv.2006.06.065

X. Liu, N. Vlajic, X. Long, G. Meng, and B. Balachandran, Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects, Nonlinear Dynamics, vol.10, issue.3, pp.61-77, 2013.
DOI : 10.1007/s11071-012-0690-x

N. M. Newmark, A method of computation for structural dynamics, Journal of the Engineering Mechanics Division, vol.85, pp.67-94, 1959.

J. N. Reddy, On locking-free shear deformable beam finite elements, Computer Methods in Applied Mechanics and Engineering, vol.149, issue.1-4, pp.113-132, 1997.
DOI : 10.1016/S0045-7825(97)00075-3

T. G. Ritto, M. R. Escalante, R. Sampaio, and R. M. , Drill-string horizontal dynamics with uncertainty on the frictional force, Journal of Sound and Vibration, vol.332, issue.1, pp.145-153, 2013.
DOI : 10.1016/j.jsv.2012.08.007

T. G. Ritto, C. Soize, and R. Sampaio, Non-linear dynamics of a drill-string with uncertain model of the bit???rock interaction, International Journal of Non-Linear Mechanics, vol.44, issue.8, pp.865-876, 2009.
DOI : 10.1016/j.ijnonlinmec.2009.06.003

URL : https://hal.archives-ouvertes.fr/hal-00684337

T. G. Ritto, C. Soize, and R. Sampaio, Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model, Computational Mechanics, vol.30, issue.1, pp.415-42710, 2010.
DOI : 10.1007/s00466-009-0462-8

URL : https://hal.archives-ouvertes.fr/hal-00684321

S. M. Sahebkar, M. R. Ghazavi, S. E. Khadem, and G. M. , Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well. Mechanism and Machine Theory, pp.743-760, 2011.

G. I. Schuëller, On the treatment of uncertainties in structural mechanics and analysis, Computers & Structures, vol.85, issue.5-6, pp.235-243, 2007.
DOI : 10.1016/j.compstruc.2006.10.009

C. Soize, Stochastic modeling of uncertainties in computational structural dynamics???Recent theoretical advances, Journal of Sound and Vibration, vol.332, issue.10, pp.2379-2395
DOI : 10.1016/j.jsv.2011.10.010

URL : https://hal.archives-ouvertes.fr/hal-00743699

P. D. Spanos, A. M. Chevallier, N. P. Politis, and M. L. Payne, Oil and gas well drilling: a vibrations perspective. The Shock and Vibration Digest, pp.85-103, 2003.
DOI : 10.1177/0583102403035002564