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The main goal of this research is to analyse the effects of drilling mud flow rate, drill string weight, weight on bit and angular velocity on stability and vibration of drill string. To this end, kinetic and potential energies of a rotating drill string are written while axial and lateral vibrations are considered. The effects drill string's Weight, weight on bit and geometrical shortening are considered in the model. Drilling mud's effects are modelled by the Paidoussis formulations. Finite element method is employed to discrete the formulations. The stabilizers are modelled by dropping the coincided nodes. Linear (Flutter method) and nonlinear meth–ods are employed to analyse drill string’s stability for different weight on bit, angular veloci–ty, drilling mud flow rate and numbers and arrangements of stabilizers. These results repre–sent the significant effects of nonlinear terms. Also, the effects of drilling mud flow rate and weight on bit on the natural frequencies and time responses are illustrated. Increasing drilling mud flow rate causes decreasing of natural frequencies and vibrational amplitude. Also in–creasing weight on bit leads to decreasing natural frequencies and increasing vibrational am–plitude. These formulations can be used to choose the safe working conditions in drilling process.<\div>

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