Coupled transverse vibration modeling of drillstrings subjected to torque and spatially varying axial

Predicting and mitigating unwanted vibration of drillstrings is an important subject for oil drilling companies. Uncontrolled vibrations cause premature failure of the drillstring and associated components. The drillstring is a long slender structure that vibrates in three primary coupled modes: torsional, axial and transverse. Among these coupled modes, the transverse mode is the major cause of drillstring failures and wellbore washout. Modal analysis of drillstrings reveals critical frequencies and helps drillers to avoid running the bit near critical modes. In this article, the coupled orthogonal modes of transverse vibration of a drillstring in the presence of torque and spatially varying axial force (due to mud hydrostatic effect, self-weight and hook load) are derived and the mode shapes and natural frequencies are determined through the expanded Galerkin method. The results are verified by the nonlinear finite element method. Modal mass participation factor, which represents how strongly a specific mode contributes to the motion in a certain direction, is used to determine the appropriate number of modes to retain so that computational efficiency can be maximized.