Dynamics of a distributed drill string system: Characteristic parameters and stability maps

Ulf Jakob F. Aarsnes*, Nathan van de Wouw

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

54 Citations (Scopus)


This paper involves the dynamic (stability) analysis of distributed drill-string systems. A minimal set of parameters characterizing the linearized, axial-torsional dynamics of a distributed drill string coupled through the bit-rock interaction is derived. This is found to correspond to five parameters for a simple drill string and eight parameters for a two-sectioned drill-string (e.g., corresponding to the pipe and collar sections of a drilling system). These dynamic characterizations are used to plot the inverse gain margin of the system, parametrized in the non-dimensional parameters, effectively creating a stability map covering the full range of realistic physical parameters. This analysis reveals a complex spectrum of dynamics not evident in stability analysis with lumped models, thus indicating the importance of analysis using distributed models. Moreover, it reveals trends concerning stability properties depending on key system parameters useful in the context of system and control design aiming at the mitigation of vibrations.

Original languageEnglish
Pages (from-to)376-412
JournalJournal of Sound and Vibration
Publication statusPublished - 2018


  • Delay equations
  • Distributed systems
  • Drill-string vibrations
  • Infinite dimensional systems
  • Stability
  • Stick-slip


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