In this paper a nonlinear dynamic model for drill string in inclined well drilling is developed. Effects of drilling mud flow rate, weight on bit, angular velocity along with viscous damping on stability and vibration of the drill string are studied. Findings indicate the nonlinear effects are significant on the results. The effects of drilling mud flow rate and weight on bit on the natural frequencies and time responses are evaluated. Enhancement of drilling mud flow rate results in decreasing

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... of natural frequencies and vibrational amplitude, while increasing the weight on bit, leads to decrease of the natural frequencies and increase the vibrational amplitude.