Vibration Confinement Phenomena in Disordered, Mono-Coupled, Multi-Span Beams

[+] Author and Article Information
D. Bouzit, C. Pierre

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Vib. Acoust 114(4), 521-530 (Oct 01, 1992) (10 pages) doi:10.1115/1.2930294 History: Received January 01, 1991; Revised February 01, 1992; Online June 17, 2008


The effects of small, periodicity-destroying irregularities on the dynamics of multi-span beams are examined. It is shown that minute deviations of the span lengths from an ideal value alter qualitatively the dynamic response by localizing vibrations and waves to small geometric regions. These confinement phenomena are studied over a wide frequency range for beams resting on simple supports and with variable interspan coupling. Approximations of the localization factor (the average rate of spatial exponential decay of the vibration amplitude) are derived by statistical perturbation methods and validated by Monte Carlo simulations. If the interspan coupling is strong, localization effects are weak and of no practical significance for most engineering structures. On the other hand, localization is severe for small interspan coupling. Confinement is also generally stronger near the edges of frequency passbands and increases nearly linearly with frequency from passband to passband. This means that strong localization occurs at high frequencies, even for large static coupling between spans.

Copyright © 1992 by The American Society of Mechanical Engineers
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