Coupled axial and transverse vibrations of oilwell drillstrings

Transverse vibrations of drillstrings caused by axial loading and impact with the wellbore wall is studied. The drillstring is modeled as a slender beam with a simply-supported lower part. The Assumed Modes Method is used to obtain the governing equations of motion. Non-linear coupling terms are retained in the formulation which leads to full coupling between the axial and transverse vibration modes. The Hertzian contact theory is used to model impacts between the drillstring and the wellbore wall. The governing non-linear equations are solved numerically to obtain the response. Simulation studies are used to compare the dynamic response obtained from both fully coupled and uncoupled models. Significant differences between the two models are observed. The coupled model yields an unstable behavior at a lower load than the uncoupled model, and the subsequent response is not periodic. (C) 1996 Academic Press Limited