On the Free Vibrations of Variable-Arc-Length Beams: Analytical and Experimental
Publication: Journal of Structural Engineering
Volume 132, Issue 5
Abstract
Vibrations of horizontal, variable-arc-length beams considering the effects of large initial static sag deflections due to self weight are investigated. The variability in beam arc length arises from one end being pinned, and the other end being supported by a frictionless roller at a fixed distance from the pinned end. Using Lagrange’s equation, the large amplitude, free-vibration, equation of motion can be derived and simplified for small amplitude motion. These formulations represent small amplitude vibration about the large deformed static sag configurations. A solution is obtained by using the nonlinear finite element method. The vibration eigenvalue problem is solved using inverse iteration techniques to obtain the natural frequencies and corresponding mode shapes. Free and forced vibration experimental studies were conducted. Frequencies and mode shapes are shown for a range of beam specimens to complement the analytical results.
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Acknowledgments
This work has been sponsored by the Thailand Research Fund (TRF) under Grant No. UNSPECIFIEDPHD/00164/2541. Moreover, the first writer gratefully acknowledges the Department of Civil and Environmental Engineering, Utah State University for providing the facilities and Assistant Professor James A. Bay for his valuable advice.
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Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 132 • Issue 5 • May 2006
Pages: 772 - 780
Copyright
© 2006 ASCE.
History
Received: Jun 24, 2003
Accepted: Jul 19, 2005
Published online: May 1, 2006
Published in print: May 2006
Notes
Note. Associate Editor: Abhinav Gupta
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