Vibration analysis of drillstrings with self-excited stick-slip oscillations

Y. A. Khulief*, F. A. Al-Sulaiman, S. Bashmal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

175 Scopus citations


Drillstring vibration is one of the major causes for a deteriorated drilling performance. Field experience revealed that it is crucial to understand the complex vibrational mechanisms experienced by a drilling system in order to better control its functional operation and improve its performance. Sick-slip oscillations due to contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including the drillpipes and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangian approach in conjunction with the finite element method. The model accounts for the torsional-bending inertia coupling and the axial-bending geometric nonlinear coupling. In addition, the model accounts for the gyroscopic effect, the effect of the gravitational force field, and the stick-slip interaction forces. Explicit expressions of the finite element coefficient matrices are derived using a consistent mass formulation. The generalized eigenvalue problem is solved to determine modal transformations, which are invoked to obtain the reduced-order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate time-response of the drillstring system in the presence of stick-slip excitations.

Original languageEnglish
Pages (from-to)540-558
Number of pages19
JournalJournal of Sound and Vibration
Issue number3
StatePublished - 23 Jan 2007

Bibliographical note

Funding Information:
This research work is funded by King Abdulaziz City for Science & Technology; KACST Project No. AR-22-11. The authors greatly appreciate the support provided by KACST and King Fahd University of Petroleum & Minerals during this research.

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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