Coupled axial/torsional vibrations of drill-strings by means of non-linear model

In the present work a geometrically non-linear model is presented to study the coupling of axial and torsional vibrations on a drill-string, which is described as a vertical slender beam under axial rotation. It is known that the geometrical non-linearities play an important role in the stiffening of a beam. Here, the geometrical stiffening is analyzed using a non-linear finite element approximation, in which large rotations and non-linear strain-displacements are taken into account. The effect of structural damping is also included in the model. To help to understand these effects comparisons of the present model with linear ones were simulated. The preliminary analysis shows that linear and non-linear models differ considerably after the first periods of stick-slip. The behavior is more evident with the increase of the friction in the lower part of the drill.