Non-Linear Vibrations of Rotating Cantilever Beams

Abstract

The problem of flexural vibration of a rotating cantilever blade is non-linear when the vibration takes place in a plane other than perpendicular to the plane of rotation. The non-linearity arises from the effects of Coriolis accelerations due to the rotation of the blade mounted on the periphery of a disc. Lo and Renbarger neglected the non-linear terms in their investigation and arrived at a simple relation for the frequency of vibration in terms of the stationary frequency of the beam, the rotating speed and the orientation of the plane of vibration. Lo in his analysis simplified the non-linear problem by assuming the blade to be rigid everywhere excepting at the root and presented the solution in a phase plane. Isakson and Eisley have considered a similar model to determine the natural frequencies in coupled bending and torsion of twisted rotating cantilever blades.