The free vibration of compact rotating radial cantilevers

The free vibration of rotating uniform radial cantilever beams of compact cross section is considered, with account taken of centrifugal coupling between motions in the principal elastic planes. For cases other than those in which the principal elastic axes coincide with the equatorial and meridional planes the centrifugal coupling is shown to modify the vibrational behaviour of the compact beam when compared to that of a beam which is infinitely stiff in one principal plane and can result in a considerable reduction in fundamental natural frequency. Results are presented which show how the natural frequencies and mode shapes of the lower modes vary with spin speed for various root offset and cross-sectional configurations.