The Influence of Dynamical Imperfection on the Vibration of Rotating Disks

Abstract

This paper is concerned with the vibration of disks particularly the form known as the ‘stationary wave’ which can develop in a rotating disk by the application of a stationary axial force at the periphery. The forms of vibration involving n nodal diameters are considered, and phenomena associated with linear and non-linear free and forced vibration are discussed in detail. Thereafter, attention is focused on the behaviour of real disks which, owing to inevitable imperfection, possess two independent modes of vibration, and thus two natural frequencies, for each value of n. It is shown that the stationary wave is greatly influenced by the degree of imperfection present. Experimental studies with stationary and rotating disks are presented covering forced vibration in the linear and nonlinear zones. The results show that a non-linear stationary wave may exist in a rotating disk over a wide speed range depending on the magnitude of the applied force. As speed increases this wave finally collapses and in doing so becomes a travelling wave which accelerates slowly in the direction of disk rotation as its amplitude subsides. Experiments conducted with large artificial imperfection show that the stationary wave may be transformed into two modes of vibration which are fixed in position in the disk. These modes resonate separately at their respective frequencies and apparently suffer a high degree of aerodynamic damping due to rotation. The magnitude of disk vibration is thus greatly reduced by the introduction of imperfection. Short mathematical appendices are included which contain the main theoretical results.