Modelling of Coupled Nonlinear Axial and Lateral Vibrations of Drill Strings
70 77
Keywords:
drill string, nonlinear model, axial and lateral vibrations, rod, the Bubnov-Galerkin method, stiffness switching methodAbstract
In this work a nonlinear mathematical model of coupled axial and lateral vibrations of a drill string under the effect of a longitudinal compressing force is investigated. The drill string is modelled in the form of a rotating elastic rod. To solve the model the Bubnov-Galerkin method and numerical stiffness switching method are applied. It is shown that the coupled axial and lateral vibrations of the drill string only arise at odd frequencies in Bubnov-Galerkin's expansion. Numerical analysis of the influence of the drill string geometrical and frequency characteristics on its vibrations is carried out, and the corresponding recommendations are provided.References
1. Al-Hiddabi S.A., Samanta B., Seibi A. Non-linear control of torsional and bending vibrations of oilwell drillstrings // J. Sound and Vibration. – 2003. – Vol. 265. – P. 401-415.
2. Neskoromnykh V.V. Destruction of rocks while exploration. – Krasnoyarsk: SFU, 2012. – 298 p. (in Russian)
3. Yigit A.S., Christoforou A.P. Coupled axial and transverse vibrations of oilwell drillstrings // J. Sound and Vibration. – 1996. – Vol. 195, No. 4. – P. 617-627.
4. Christoforou A.P., Yigit A.S. Dynamic modeling of rotating drillstrings with borehole interactions // J. Sound and Vibration. – 1997. – Vol. 206, No. 2. – P. 243-260.
5. Melakhessou H., Berlioz A., Ferraris G. A nonlinear well-drillstring interaction model // Transactions of the ASME. – 2003. – Vol. 125. – P. 46-52.
6. Novozhilov V.V. Foundations of the Nonlinear Theory of Elasticity. – Moscow-Leningrad: OGIZ, 1948. – 211 p. (in Russian)
7. Demidov S.P. Theory of elasticity. – Moscow: Vysshaya Shkola, 1979. – 431 p. (in Russian)
8. Khajiyeva L.A., Kudaibergenov A.K. Modeling of nonlinear dynamics of drill strings in a supersonic air flow // 5th Int. Symposium on Knowledge Aquisition and Modeling (KAM 2015). – London, Great Britain, June 27-28, 2015 (in press).
9. Erofeev V.I., Zinchenko A.S. Nonlinear flexural and longitudinal flexural wave propagation in an elastic rod // Vestnik of Lobachevsky University of Nizhni Novgorod. – 2012. – No. 5 (2). – P. 81-83. (in Russian)
10. Vaz M.A., Patel M.N. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. // Engineering structures. – 1995. – Vol. 17 (6). – P. 437-442.
11. Khajiyeva L., Kudaibergenov A., Kudaibergenov A., Kydyrbekuly A. Analysis of drill string motion in a gas stream // Proc. 8th European Nonlinear Dynamics Conf. (ENOC 2014). - Vienna, Austria, 2014.
12. Kudaibergenov A.K., Kudaibergenov Ask.K. Comparative analysis of numerical methods for modeling of drill string nonlinear dynamics // Izvestiya NAN RK, phys.-mat. series. – 2015. – No. 3 (301). – P. 37-42. (in Russian)
2. Neskoromnykh V.V. Destruction of rocks while exploration. – Krasnoyarsk: SFU, 2012. – 298 p. (in Russian)
3. Yigit A.S., Christoforou A.P. Coupled axial and transverse vibrations of oilwell drillstrings // J. Sound and Vibration. – 1996. – Vol. 195, No. 4. – P. 617-627.
4. Christoforou A.P., Yigit A.S. Dynamic modeling of rotating drillstrings with borehole interactions // J. Sound and Vibration. – 1997. – Vol. 206, No. 2. – P. 243-260.
5. Melakhessou H., Berlioz A., Ferraris G. A nonlinear well-drillstring interaction model // Transactions of the ASME. – 2003. – Vol. 125. – P. 46-52.
6. Novozhilov V.V. Foundations of the Nonlinear Theory of Elasticity. – Moscow-Leningrad: OGIZ, 1948. – 211 p. (in Russian)
7. Demidov S.P. Theory of elasticity. – Moscow: Vysshaya Shkola, 1979. – 431 p. (in Russian)
8. Khajiyeva L.A., Kudaibergenov A.K. Modeling of nonlinear dynamics of drill strings in a supersonic air flow // 5th Int. Symposium on Knowledge Aquisition and Modeling (KAM 2015). – London, Great Britain, June 27-28, 2015 (in press).
9. Erofeev V.I., Zinchenko A.S. Nonlinear flexural and longitudinal flexural wave propagation in an elastic rod // Vestnik of Lobachevsky University of Nizhni Novgorod. – 2012. – No. 5 (2). – P. 81-83. (in Russian)
10. Vaz M.A., Patel M.N. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. // Engineering structures. – 1995. – Vol. 17 (6). – P. 437-442.
11. Khajiyeva L., Kudaibergenov A., Kudaibergenov A., Kydyrbekuly A. Analysis of drill string motion in a gas stream // Proc. 8th European Nonlinear Dynamics Conf. (ENOC 2014). - Vienna, Austria, 2014.
12. Kudaibergenov A.K., Kudaibergenov Ask.K. Comparative analysis of numerical methods for modeling of drill string nonlinear dynamics // Izvestiya NAN RK, phys.-mat. series. – 2015. – No. 3 (301). – P. 37-42. (in Russian)
Downloads
How to Cite
Kudaibergenov, A. K., & Kudaibergenov, A. K. (2015). Modelling of Coupled Nonlinear Axial and Lateral Vibrations of Drill Strings. International Journal of Mathematics and Physics, 6(2), 27–35. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/145
Issue
Section
Informatics and Mathematical Modeling
