A three-nodal, C0 Timoshenko beam finite element model is applied to analyze the natural whirl speeds of a rotating shaft with different end conditions. The effects of translational and rotary inertia, gyroscopic moments, bending and shear deformation are included in the mathematical model. In order to facilitate the calculations of the natural whirl speeds, a rotating frame of reference is used in the formulation. Comparison is made of the present finite element analysis with other previously published works available in the literature, with results presented for the case of forward and backward precession to verify the gyroscopic effects. The numerical results show that the present finite element model has high accuracy and good convergence.
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