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Nonlinear dynamics of torsional waves in a drill-string model with spatial extent

Research output: Working paperWorking paper and Preprints

Original languageEnglish
StatePublished - 28 Feb 2007


In this paper we investigate the dynamics and bifurcations of an oil-well drill-string model that takes the form of a neutral delay differential equation (NDDE). We consider the torsional mode of the drill-string and investigate the associated stick-slip motion. To analyse the model we develop numerical continuation routines based on Fourier-methods since existing routines based on polynomial approximations are unable to cope with the presence of arbitrarily weakly damped modes. We find `resonance peaks' in the dynamics where a high-frequency mode is superimposed on the underlying periodic behaviour causing large torsional waves in the drill-string. We show that the resonance peaks are robust to small perturbations in the friction parameters but disappear if static friction forces are neglected completely

Additional information

Sponsorship: David A.W. Barton is a research fellow funded by the Lloyds Tercentenary Foundation

    Research areas

  • delay differential equation, Cosserat, bifurcation, numerical continuation

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  • BKW07-JVC

    Submitted manuscript, 1 MB, PDF-document


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