Free Vibration of a Rotating Elastic Body: The General Theory and Some Examples of Practical Cases

Abstract

ENGINEERING science provides many examples of the vibration of rotating bodies. The torsional vibration of crankshafts, the whirling of shafts and rotors and the flexural vibration of propeller blades are some of them. Satisfactory theoretical treatments have been given for most of such problems, but so far as the writer knows no attempt has been made before to derive general equations for the vibration of a rotating body. In this paper such equations arc obtained. In as much as the understanding of any problem is helped if its relation to other problems is appreciated, it follows that the study of general equations is useful to the student of engineering. The equations have another use when particular problems, which have not yet received a special treatment of their own, are being considered; the general equations then enable relationships between the new problems and other previously treated problems to be seen and qualitative predictions of the effects of the different terms in the equations can then be made. An example of this occurs in the study of the vibration of a rotating bell or cup, such as is formed by some internally toothed gear wheels; further reference to this will be made later.

Citation

Johnson, D.C. (1952), "Free Vibration of a Rotating Elastic Body: The General Theory and Some Examples of Practical Cases", Aircraft Engineering and Aerospace Technology, Vol. 24 No. 8, pp. 234-236. https://doi.org/10.1108/eb032192