Effect of Small Hub-Radius Change on Bending Frequencies of a Rotating Beam

Abstract

By the method of perturbation, a simple relation is formulated for the determination of the change of bending frequencies of a rotating beam due to a small change of hub radius. The first-order solution shows that a frequency parameter γ is a linear function of the hub-radius change and the constant of proportionality is readily obtainable from known parameters. The frequency ω itself can also be represented by a linear function of the hub-radius change. This confirms the results previously obtained by Boyce by repeated solutions of the differential equations for a particular beam. Higher-order solutions are also established and shown to be convergent within the limitation imposed on the amount of the hub-radius change allowable.