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

P. D. Spanos, A. M. Chevallier, and N. P. Politis, Nonlinear Stochastic Drill-String Vibrations, Journal of Vibration and Acoustics, vol.124, issue.4, pp.512-51810, 2002.
DOI : 10.1115/1.1502669

M. A. Trindade, C. Wolter, and R. Sampaio, Karhunen???Lo??ve decomposition of coupled axial/bending vibrations of beams subject to impacts, Journal of Sound and Vibration, vol.279, issue.3-5, pp.1015-1036, 2005.
DOI : 10.1016/j.jsv.2003.11.057

R. Sampaio, M. T. Piovan, G. Venero, and . Lozano, Coupled axial/torsional vibrations of drill-strings by means of non-linear model, Mechanics Research Communications, vol.34, issue.5-6, pp.497-502, 2007.
DOI : 10.1016/j.mechrescom.2007.03.005

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, Stochastic dynamics of a drill-string with uncertain weight-on-hook, Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol.32, issue.3, pp.250-25810, 1590.
DOI : 10.1590/S1678-58782010000300008
URL : https://hal.archives-ouvertes.fr/hal-00684313

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

T. G. Ritto and R. Sampaio, STOCHASTIC DRILL-STRING DYNAMICS WITH UNCERTAINTY ON THE IMPOSED SPEED AND ON THE BIT-ROCK PARAMETERS, International Journal for Uncertainty Quantification, vol.2, issue.2, pp.111-124, 2012.
DOI : 10.1615/Int.J.UncertaintyQuantification.v2.i2.30

T. G. Ritto, M. R. Escalante, R. Sampaio, and M. B. Rosales, 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

G. Gilardi and I. Sharf, Literature survey of contact dynamics modelling Mechanism and Machine Theory, pp.1213-123910, 2002.

K. H. Hunt, F. E. Crossley, and T. J. Hughes, 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

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

G. I. Schuëller, A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, issue.4, pp.197-321, 1997.
DOI : 10.1016/S0266-8920(97)00003-9

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, 2013.
DOI : 10.1016/j.jsv.2011.10.010
URL : https://hal.archives-ouvertes.fr/hal-00743699