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

DAW Barton, B Krauskopf, RE Wilson

Research output: Working paperWorking paper and Preprints

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Abstract

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
Original languageEnglish
Publication statusPublished - 28 Feb 2007

Bibliographical note

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

Keywords

  • delay differential equation
  • Cosserat
  • bifurcation
  • numerical continuation

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