Vibration and Balancing of Rotating Continuous Shafts

Abstract

A general theoretical treatment is presented of the vibration of rotating shafts supported on any number of bearings. The shafts may be of uniform or non-uniform cross-section and the bearings may be flexible. While it is assumed that the system is axially symmetric, the defects of lack of balance and of initial bend in the shaft are both admitted and the effects of self-weight may be readily allowed for. It is shown that, in principle, continuous shafts bring nothing new to the theory of shafts supported only at their two ends; in particular, they may be balanced in the same way. The relevance of this to the dynamics of turbo-alternators is pointed out and a logical basis for experiments in balancing these machines is described. Incidental to the treatment of rotating shafts are several new, general results in the transverse vibration of non-rotating continuous beams.