Non-linear Vibrational Analysis of an Axially Moving Drillstring System with Time Dependent Axial Load and Velocity in an Inclined Well

A non-linear model of a drill string system in an inclined well with axially moving motion and loading is established and analyzed by perturbation technique. The drillstring is modeled as a simply supported axially moving rotor. Based on Hamilton's principle, the dynamic model developed consists of kinetic and potential energy. Non-linear coupling terms are kept in the formulation, which leads to full coupling between the axial and the transverse vibrational modes. The method of multiple scales is employed to solve the non-linear equations, to analyze the steady state response, and to find the stability region of the system. Analytical and numerical results reveal the non-linear phenomena, such as primary and parametric resonance that have not been previously reported. Our results are compared with some existing experimental date showing relatively good agreements.