Vibrations of Rotating Cantilever Blading: Theoretical Approaches to the Frequency Problem Based on Energy Methods

Abstract

A theoretical expression is obtained for the work done due to centrifugal effects when a rotating cantilever blade executes small vibrations. The total potential energy and kinetic energy of the system are formulated, use being made of previously derived expressions for the stationary blade. By use of Rayleigh's method an equation for the fundamental frequency of vibration is established and, for the case of a straight blade of uniform and symmetrical cross-section, a solution is deduced based on an approximate shape for the normal elastic curve. The characteristic differential equations of motion for the rotating system are obtained from the energy expressions by use of variational calculus. Coriolis effects, being small, can be neglected in the analyses.