Dynamic characterization of a flexible internally damped spinning shaft with constant eccentricity

In the present study, the dynamic characterization of a flexible spinning shaft with constant eccentricity driven by a non-ideal energy source (DC motor) with external and internal damping has been focused. It is well established that the structural response of a vibratory system to which a non-ideal drive is connected may act as an energy sink under certain conditions such that a part of the energy supplied by the source is spent to vibrate the structure rather than to increase the drive speed. This phenomenon is formally known as the Sommerfeld effect. The Sommerfeld effect characterized by jump phenomena is studied through the steady-state amplitude obtained by instantaneous power balance method and further verified through numerical simulation. Finally, power balance equation is transformed into a characteristic equation through which jump phenomena and Sommerfeld effect are predicted numerically for the first and third modes using root loci method. The break-in and breakaway points of the root loci represent the values of the supply voltage at which jumps in shaft speed and flexural vibration amplitudes take place during coast-up and coast-down operation.