Abstract
The forced response of a spinning disk under space-fixed couples is analyzed analytically using the eigenfunction expansion method. A general couple on the disk surface can be divided into two components, i.e., pitching (with moment axis in the radial direction) and rolling (with moment axis in the circumferential direction). Both the transient vibration and the steady state deflection of the spinning disk are presented, with emphasis on the effects of the rotation speed and external damping. Two types of external damping are considered; one is rotating with the disk and the other is space-fixed. It is found that in the sub-critical speed range, both the rotating and space-fixed dampings tend to suppress the transient response of a spinning disk under a space-fixed pitching couple. On the other hand, in the super critical speed range, the rotating damping tends to suppress the transient vibration while the spaced-fixed damping tends to destabilize the system.
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