Bending Vibrations of a Class of Rotating Beams with Hypergeometric Solutions

Abstract

We study the transverse deflections of a straight tapered symmetric beam attached to a rotating hub as a model for the bending vibration of blades in turbomachinery. A broad class of blade shapes is obtained for which the equation of motion can be solved analytically in terms of hypergeometric functions. Based on this analytic solution, an algorithm for computing the natural bending frequencies and mode shapes as a function of setting angle and rotation rate is presented and applied to an example.