عنوان مقاله [English]
In this paper, the effect of drilling mud and its velocity on the vibration of drill string is studied. Considering drill string weight, weight on bit, borehole interaction, and drilling mud forces, the vibrational equations of drill string in axial and lateral directions are derived. These equations are derived by kinetic and potential energy of drill string and the works of external forces. Using mode summation methods and Lagrangian formula, these equations with partial derivative are converted to equations with time derivative. By these equations, the drilling mud flow rate and weight on bit, which lead to drill string buckling, can be found. Natural frequencies, drilling mud flow rate, and weight on bit for buckling are verified by the validated results. The results show that the natural frequencies decrease as the drilling mud flow rate increases. Also, drilling mud acts as mass and damper; these effects of drilling mud increase as drilling mud flow rate rises. These effects cause more damping in drill string vibration in both pre-buckling and post-buckling.