Forced Harmonic Response of a Continuous System Displaying Eigenvalue Veering Phenomena

[+] Author and Article Information
J. H. Ginsberg, Hoang Pham

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Vib. Acoust 117(4), 439-444 (Oct 01, 1995) (6 pages) doi:10.1115/1.2874476 History: Received February 01, 1993; Revised January 01, 1994; Online February 26, 2008


Prior studies of self-adjoint linear vibratory systems have extensively explored the free vibration phenomena associated with veering of eigenvalue loci that depict the dependence of natural frequencies on a system parameter. The present work is an exploration of the effect of such phenomena on the response of a nearly-periodic continuum to harmonic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pin support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state response to a harmonic concentrated force applied to the middle of one span. The modal equations are used to identify situations in which the force response is localized to one span, as well as the degree to which the location and magnitude of the peak displacement display parameter sensitivity. The effect of hysteretic loss on forced localization is discussed.

Copyright © 1995 by The American Society of Mechanical Engineers
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