Vibration of a Spinning Annular Disk With Coupled Rigid-Body Motion

Abstract

The vibration of a spinning annular disk with coupled translational and rotational rigid-body motion is analyzed. The spinning disk, with one linear spring as transverse load, is free to translate and rotate relative to the shaft axis. Modal functions of a stationary annular disk are used to describe the elastic displacement of the spinning disk. The governing equation includes the rigid disk translation, rotation, and the flexible disk vibration. Coupling effects between the rigid-body motion and the annular disk modal function are identified in the formulation. Because of the coupling effects, stable operation beyond divergence (critical speed) is achieved, the disk loses its stability to flutter. This stability prediction is different from that of a spinning disk without rigid-body motion where the disk is unstable at and right after divergence.