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

[+] Author and Article Information
Hsu Lo

Purdue University, Lafayette, Indiana

J. E. Goldberg, J. L. Bogdanoff

Purdue University

J. Appl. Mech 27(3), 548-550 (Sep 01, 1960) (3 pages) doi:10.1115/1.3644038 History: Received January 13, 1958; Revised December 29, 1959; Online September 16, 2011


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.

Copyright © 1960 by ASME
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