Abstract
A flexible shaft with an asymmetrical rotor exhibits a complicated change in amplitude of whirling when the shaft passes through the critical speed. The amplitude fluctuation is related to the torsional vibration of the shaft. Accordingly, analyses of the precise torsional vibration require equations of motion which hold an accuracy of the second-order of shaft deformations, shaft deflection, angle of deflection, and torsion. The driving condition of the shaft provides a constant angular acceleration. The present asymptotic solution demonstrates that the torsional vibration resonates at two rotating speeds immediately after the rotating shaft passes the critical speed of whirling. One of these resonance points appears owing to the asymmetry of rotor. The maximum amplitude increases and decreases alternately as the angular acceleration is changed monotonously.
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