The vibration of drill string system may reduce the life of the used pipes and tools by accelerating the process of crack propagation and fatigue. Furthermore, undesired vibration can cause pipes and tools failure, wash-outs and diminish in the infiltration rate practically. In applied and engineering sciences, the vibration is one of the most important factors in designing, operation and lifetime of the drill strings. So, study on nonlinear vibrations in drill string such as every other rotary machine is essential and vital. The drill string costs may be diminished using recent technologies which make the drilling process more professional and beneficial. Drill string vibrations are usually intricate because all axial, lateral and torsional vibrations are present and coupled linearly and nonlinearly [1,2]. For instance, stick-slip torsional motion cause high bit speed level which excite severe axial and lateral vibrations [3]. To solve this, one can increase rotary table speed beyond a threshold value, because stick-slip vibrations are self-excited, but this solu-
AbstractA vibrant model for drill string in inclined well drilling is presented. Also, the effects of weight on bit, drilling mud flow rate and vibration of the drill string are analyzed analytically. The vibrations of drill string may bind optimizing the power and advantages of drill string that is an important problem for optimization and design of it. Dynamic equation of the model is introduced with consider of the axial displacement and lateral bending geometric nonlinear coupling. The effect of drilling mud flow is modeled using Paidoussis formulations considering energy formulation. Equation of the motion for the rotating drill string is derived utilizing Lagrangian technique and implementing FEM to analyze and solve these equations. The obtained outcomes show the nonlinear effects are important on the obtained results and findings. The effects of the drilling mud flow rate and weight on bit on the natural frequencies and time responses are evaluated. Improvement and development of the drilling mud flow rate results in decreasing of natural frequencies and vibrational amplitude, while increasing the weight on bit, leads to reduce of the natural frequencies and enhance the vibration amplitude clearly.