Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam

[+] Author and Article Information
D. C. Kammer

Structural Dynamics Research Corporation, San Diego, CA 92121

A. L. Schlack

Department of Engineering Mechanics, University of Wisconsin—Madison, Madison, Wisconsin 53706

J. Appl. Mech 54(2), 305-310 (Jun 01, 1987) (6 pages) doi:10.1115/1.3173012 History: Received April 29, 1986; Revised October 16, 1986; Online July 21, 2009


The effects of a time-dependent angular velocity upon the vibration of a rotating Euler beam are presented. It is assumed that the angular velocity can be expressed as the sum of a steady-state value and a relatively small periodic perturbation. Equations of motion are derived for a beam oriented parallel to the spin axis. Terms with time-dependent coefficients appear in the equations of motion due to the nonconstant spin rate resulting in a nonautonomous system possessing parametric instabilities. A perturbation technique called the KBM method is used to derive general expressions for approximate solutions and instability region boundaries. A simple perturbation function is assumed for the purpose of illustrating the use of the derived general expressions.

Copyright © 1987 by ASME
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