An analysis is developed to include the effect of disk flexibility and gyroscopic forces on the resonant frequencies of an axisymetric rotating shaft with multiple disks and bearings. The shaft and disks are divided into constant-section segments with lumped masses. A transfer matrix analysis is used to obtain the resonant frequencies and mode shapes for linear, undamped, circular orbit motion. Several diverse rotor and disk configurations are studied with a range of disk stiffnesses at rotating speeds from zero to synchronous whirl speed. It is found that disk flexibility can significantly reduce the rotor resonant speeds, particularly at low speed. Some general conclusions and first-approximation methods are presented.

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