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. Stick-slip oscillations due to contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A multibody dynamic model of the drilling system including the drillpipes, drillcollars, and the rotary drive is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach in conjunction with the finite element method. The model accounts for the gyroscopic effect, the inertia coupling, the effect of the gravitational force field, and the stick-slip interaction forces. Explicit expressions of the finite element inertia coupling and axial stiffening matrices are derived using a consistent mass formulation. Modal transformations are invoked to obtain a 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.

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