Vibration of a Rotating Cylindrical Shell

Abstract

In this paper, the state of vibration of a circular cylindrical shell which is rotating about its axis with a constant angular velocity is discussed utilizing the fundamental differential equation introduced by the present author. The same problem has researched by G.H. Bryan⁽¹⁾ ; the utilization of his results, however, is very limited because of his assumption of inextensionality. In this paper, no such limitation is imposed and several problems which cannot be solved by Bryan's method are exhibited. The relations between the angular velocities of the nodes and those of the shells in various wave patterns are obtained, and in the particular case where the shell vibrates as a beam, the relation between the critical speed and the natural frequency is also discussed.