Symmetric Planar Vibrations of a Rotating Disk

Abstract

The complete problem of coupled symmetric radial and torsional vibrations of a thin, rotating, circular disk has been solved, using undeformed coordinates. The formulation of the problem used here yields several interesting and previously unreported results for the static problem. Two types of instabilities occur: “static resonances” and classical instabilities, for which radial and torsional displacements everywhere in the disk can become unboundedly large. These resonances have been explained physically. The solutions of the frequency equation and the mode shapes are obtained. The effect of rotation is to lower the natural frequencies of the disk. When deformed coordinates are used, as is the case in the classical analysis of a rotating disk, the instabilities are concealed.