T. Richard, C. Germay, and E. Detournay Self-excited stick-slip oscillations of drill bits C. R. Méc. French Acad. Sci. 332 2004 619 626 10.1016/j.crme.2004.01.016
T. Richard, C. Germay, and E. Detournay A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits J. Sound Vib. 305 3 2007 432 456 10.1016/j.jsv.2007.04.015
D.R. Pavone, J.P. Desplans, Application of high sampling rate downhole measurements for analysis and cure of stick-slip in drilling, SPE 28324, 1994.
J.F. Brett The genesis of torsional drillstring vibrations SPE Drilling Eng. 1992 168 174
J. Jansen, L. vandenSteen, and E. Zachariasen Active damping of torsional drillstring vibrations with a hydraulic top drive SPE Drilling Completion 1995 250 254
V.A. Palmov, E. Brommundt, and A.K. Belyaev Stability analysis of drillstring rotation Dyn. Stability Syst. 10 2 1995 99 110 10.1080/ 02681119508806197
R.W. Tucker, and C. Wang An integrated model for drill-string dynamics J. Sound Vib. 224 1 1999 123 165 10.1006/jsvi.1999.2169
N. Challamel Rock destruction effect on the stability of a drilling structure J. Sound Vib. 233 2 2000 235 254 10.1006/jsvi.1999.2811
A.G. Balanov, N.B. Janson, P.V.E. McClintock, R.W. Tucker, and C.H.T. Wang Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill-string Chaos Solitons Fractals 15 2 2003 381 394 10.1016/S0960-0779(02)00105-4
A.S. Yigit, and A.P. Christoforou Stick-slip and bit-bounce interaction in oil-well drillstrings ASME J. Energy Resour. Technol. 128 4 2006 268 274 10.1115/1.2358141
E. Detournay, and P. Defourny A phenomenological model of the drilling action of drag bits Int. J. Rock Mech. Min. Sci. 29 1 1992 13 23
C. Germay, V. Denoel, and E. Detournay Multiple mode analysis of the self-excited vibrations of rotary drilling systems J. Sound Vib. 325 1-2 2009 362 381 10.1016/j.jsv.2009.03.017
B. Besselink, N. van de Wouw, and H. Nijmeijer A semi-analytical study of stick-slip oscillations in drilling systems J. Comput. Nonlinear Dyn. 6 2 2011 10.1115/1.4002386 021006-1-9
K. Nandakumar, and M. Wiercigroch Stability analysis of a state dependent delayed, coupled two DOF model of drill-string vibration J. Sound Vib. 332 10 2013 2575 2592 10.1016/j.jsv.2012.12.020
K. Nandakumar, and M. Wiercigroch Galerkin projections for state-dependent delay differential equations with applications to drilling Appl. Math. Modelling 37 4 2013 1705 1722 10.1016/j.apm.2012.04.038
T. Insperger, G. Stépán, J. Turi, State-dependent delay model for regenerative cutting processes, Proceedings of Fifth EUROMECH Nonlinear Dynamics Conference, ENOC 2005, Eindhoven, Netherlands, 2005, pp. 1124-1129.
T. Insperger, G. Stépán, and J. Turi State-dependent delay in regenerative turning processes Nonlinear Dyn. 47 2007 275 283 10.1007/s11071-006-9068-2
T. Insperger, D. Barton, and G. Stépán Criticality of Hopf bifurcation in state-dependent delay model of turning processes Int. J. Non-Linear Mech. 43 2008 140 149 10.1016/j.ijnonlinmec.2007.11.002
C. Germay, N. van de Wouw, H. Nijmeijer, and R. Sepulchre Nonlinear drillstring dynamics analysis SIAM J. Appl. Dynamical Syst. 8 2 2009 527 553 10.1137/060675848
R.I. Leine, D.H. van Campen, and W.J.G. Keultjes Stick-slip whirl interaction in drillstring dynamics J. Vib. Acoust. 124 2002 209 220 10.1115/1.1452745
E. Detournay, T. Richard, and M. Shepherd Drilling response of drag bits theory and experiment Int. J. Rock Mech. Min. Sci. 45 8 2008 1347 1360 10.1016/j.ijrmms.2008.01.010
T. Richard, F. Dagrain, E. Poyol, and E. Detournay Rock strength determination from scratch tests Eng. Geol. 147-148 2012 91 100 10.1016/j.enggeo.2012.07.011
R.I. Leine, N. van de Wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, 1st edition, Springer-Verlag, Berlin, Heidelberg, 2008.
F. Hartung, J. Turi, Linearized stability in functional differential equations with state-dependent delays, International Conference on Dynamical Systems and Differential Equations, 2000.
F. Hartung, J. Turi, Stability in a class of functional differential equations with state-dependent delays, Qualitative Problems for Differential Equations and Control Theory, Word Scientific, 1995, pp. 15-31.
T. Luzyanina, K. Engelborghs, and D. Roose Numerical bifurcation analysis of differential equations with state-dependent delay Int. J. Bifurcation Chaos 11 3 2001 737 753 10.1142/S0218127401002407
F. Hartung Linearized stability in periodic functional differential equations with state-dependent delays J. Comput. Appl. Math. 174 2 2005 201 211 10.1016/j.cam.2004.04.006
T. Carr, R. Haberman, and T. Erneux Delay-periodic solutions and their stability using averaging in delay-differential equations, with applications Physica D Nonlinear Phenom. 241 18 2012 1527 1531 10.1016/j.physd.2012.06.001
A.M. Krall On the real parts of zeros of exponential polynomials Bull. Am. Math. Soc. 70 2 1964 291 292
G. Stépàn Retarded Dynamical Systems 1989 Longman London
K. Nandakumar, M. Wiercigroch, C. Pearson, Bit-bounce and stick-slip in drill-string dynamics, in: M. Wiercigroch, G. Rega (Eds.), Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies in Engineering Design, 2010.
D. Bernstein, and G. Coon On the zeros of a class of exponential polynomials J. Math. Anal. Appl. 11 1965 205 212
D.E. Gilsinn Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter Nonlinear Dyn. 30 2002 103 154 10.1023/A:1020455821894
R.P.H. Faassen, N. van de Wouw, J.A.J. Oosterling, and H. Nijmeijer Prediction of regenerative chatter by modeling and analysis of high-speed milling Int. J. Mach. Tool Manuf. 43 2003 1437 1445 10.1016/S0890-6955(03)00171- 8
K. Engelborghs, T. Luzyanina, G. Samaey, DDE-BIFTOOL v. 2.00: A Matlab Package for Bifurcation Analysis of Delay Differential Equations, Technical Report, K.U.Leuven, 2001.
A. Depouhon, Stability of TAZ Apparatus: A Drilling Equivalent, Master's Thesis, University of Minnesota, 2007.
L. Ledgerwood, O. Hoffmann, J. Jain, C. El Hakam, C. Herbig, R. Spencer, Downhole vibration measurement, monitoring and modeling reveal stick-slip as a primary cause of pdc bit damage in today's applications, SPE 134488, 2010.