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In this paper, the intrinsic behavior of rotating Euler-Benoulli flexible shafts was studied due to coupled bending and torsional vibrations. The equations of motion of the shaft with unbalanced eccentricity and viscous material damping were derived by the Hamilton principle. The numerical solution was obtained using the perturbation approach and mode-assuming method. The influences of the coupled vibrations between the bending and torsion, the rotating speed, material damping and the slenderness ratio of the shaft were analyzed. It is clearly shown that the beating phenomena can occur when the interaction of torsion and flexure is considered.