Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well

In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques. The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton's principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system. Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented. Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system. Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data.