Bending Vibrations of a Class of Rotating Beams with Hypergeometric Solutions

[+] Author and Article Information
D. Storti, Y. Aboelnaga

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195

J. Appl. Mech 54(2), 311-314 (Jun 01, 1987) (4 pages) doi:10.1115/1.3173013 History: Received February 24, 1986; Revised July 24, 1986; Online July 21, 2009


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.

Copyright © 1987 by ASME
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