Due to the limitations of manufacturing accuracy, long cylindrical rotors used in heavy power transmission lines and paper machinery are dynamically excited by internal elastic forces. The origin of these forces is the out-of-roundness profile of the inner and outer radii of the rotor, which contributes to the bending stiffness distribution along the rotor span. Distributed anisotropy of the rotor under gravitational load is reason of the existence of half-critical speeds, on which the rotor experiences non-classical resonance state. This problem has been formulated in terms of nominal and deviated motion according to the splitting of the bending stiffness tensor in a similar way. This leads to a static rotor equation, whose amplification effect on to the dynamic part of the motion has been analyzed in details. This includes formal solution of the resulting dynamic Hill equation in terms of the modal coordinates of the corresponding free whirling Rayleigh beam.

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