ON THE IN-PLANE VIBRATION AND STABILITY OF A SPINNING ANNULAR DISK

Abstract

A comprehensive investigation of the free in-plane vibration of a spinning annular disk is presented in this paper. Emphasis is given to the effect of clamping ratio on the natural frequencies and critical speeds of the spinning disk. For a disk with small clamping ratio, the limiting speed at which the disk is allowed to rotate safely is determined by the critical speed of the axisymmetrical mode. Beyond this critical speed divergence instability will be induced. For a disk with large clamping ratio, on the other hand, the speed limit is determined by the critical speed of a mode with a large number of nodal diameters. It is observed that the critical speeds of the modes with nodal diameters approach an asymptotic value as the number of nodal diameters increases. Numerical simulations show that this asymptotic critical speed is independent of the clamping ratio, while it is dependent on the Poisson ratio of the disk.