The vibrations of a spinning disk

Abstract

1. This paper treats of the transverse vibrations of a circular disk of uniform thickness rotating about its axis with constant angular velocity. The problem has a practical bearing, as throwing light on the occasional failure of turbine disks. In an impulse turbine blades are fitted to the rim of a thin disk, and steam is admitted to them from nozzles which are usually arranged symmetrically, but not always continuously, round the periphery. The failures appear to be sometimes due to the blades coming in contact with the adjacent parts. This points to transverse vibrations, and there can be little doubt that the phenomenon is one of resonance between the periodic forces exerted by the steam jets and the periods of free vibration of the disk. For a thorough investigation it would be necessary to ascertain, to a reasonable degree of approximation, the free periods of a symmetrical disk of any given profile. This may form the theme of a subsequent investigation by one of the authors. In the meantime the study of the simpler case now discussed illustrates the physical aspects of the problem, and has suggested an important simplification in method.