The drilling industry has been suffering from huge monetary losses and non-productive time due to wear and fatigue of the drill string components. Vibration mitigation plays a pivotal role in extending the life of drill string components. The development of a comprehensive drill string vibration model will help in classifying the causes of drill string vibrations and helps in planning pro-active measures to suppress it. In the past, researchers have developed models based on factors like drill string length, axial compression load, lateral loads, shear deformation, rotary inertia and fluid damping. The four classical engineering vibration theories will be discussed in detail with the addition of fluid stiffness and fluid damping. This paper develops a drill string vibration model considering the effects of bending, translational inertia, rotary inertia, shear deformation, fluid stiffness and fluid damping. The drill string is considered as a cantilever beam of a circular cross-section immersed in water with equal pressure on both sides. The water is considered to be a spring and dash-pot model in parallel. It adopts a classical solution methodology based on D’Almbert’s principle. The eigen values, normalized mode shape, natural frequencies, orthogonality conditions and dynamic response equations are derived for all the theories. Natural Frequency and Dynamic response of the drill string are used to make informed decisions. Numerical simulation results show the influence of all the factors on vibration damping of the drill string. A critical understanding of the effects of all the above factors individually and in tandem will help in adopting a novel drilling strategy. To conclude, a complete step-by-step methodology for the proposed comprehensive drill string vibration model is put forth to determine the natural frequency and dynamic response of the drill string.

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