RESEARCH PAPERS: Vibration and Sound

Dynamic Response of a Radial Beam With Nonconstant Angular Velocity

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

SDRC, Inc., San Diego, CA 92121

A. L. Schlack

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

J. Vib., Acoust., Stress, and Reliab 109(2), 138-143 (Apr 01, 1987) (6 pages) doi:10.1115/1.3269405 History: Received August 05, 1986; Online November 23, 2009


The effects of a nonconstant angular velocity upon the vibration of a rotating Euler beam are investigated. It is assumed that the angular velocity can be written as the sum of a steady-state value and a small periodic perturbation. The time-dependence of the angular velocity results in the appearance of terms in the equations of motion which cause the system to be nonautonomous. These terms result in the existence of regions of parametric instability within which the amplitude grows exponentially. A perturbation technique called the KBM method is used to derive approximate solutions and expressions for the boundaries between stable and unstable motion. A simple perturbation function is assumed to illustrate the use of the derived general equations.

Copyright © 1987 by ASME
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