Nonlinear Free Vibrations of Suspension Bridges: Theory
Publication: Journal of Engineering Mechanics
Volume 109, Issue 1
Abstract
A general theory and analysis of the nonlinear free coupled vertical‐torsional vibrations of suspension bridges with horizontal decks are presented. Approximate solutions are developed by using the method of multiple scales via a perturbation technique. The amplitude‐frequency relationships for any single set of coupled vertical‐torsional modes are presented for three cases: (1) When the large‐amplitude vertical vibration is dominating the motion; (2) when large‐amplitude torsional vibration is dominating; and (3) when one of the linear natural frequencies of vertical vibration is equal to, or approximately equal to, another linear natural frequency of torsional vibration, and the two modes are strongly coupled; this contrasts with the linear solution, which predicts that the two modes are uncoupled.
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References
1.
Abdel‐Ghaffar, Ahmed M., and Housner, George W., “Ambient Vibration Tests of a Suspension Bridge,” Journal of Engineering Mechanics, ASCE, Vol. 104, No. EM5, Proc. Paper 14065, Oct., 1978, pp. 983–999.
2.
Abdel‐Ghaffer, Ahmed M., “Free Torsional Vibrations of Suspension Bridges,” Journal of the Structural Division, ASCE, Vol. 105, No. ST4, Proc. Paper 14535, Apr., 1979, pp. 767–788.
3.
Abdel‐Ghaffer, Ahmed M., “Vertical Vibration Analysis of Suspension Bridges,” Journal of the Structural Division, ASCE, Vol. 106, No. ST10, Proc. Paper 15759, Oct., 1980, pp. 2053–2075.
4.
Abdel‐Ghaffar, Ahmed M., “Suspension Bridge Vibration: Continuum Formulation,” Proceedings, 1980 ASCE Convention, Portland, Oregon, Apr. 14–18, Preprint 80‐018.
5.
Nayfeh, Ali H. and Mook, Dean T., Nonlinear Oscillations, John Wiley & Sons, Inc., New York, N.Y., 1979.
6.
Takahashi, K., “Non‐Linear Free Vibrations of Inextensible Beams,” Journal of Sound and Vibration, Vol. 64, Jan., 1979, pp. 31–34.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 109 • Issue 1 • February 1983
Pages: 313 - 329
Copyright
Copyright © 1983 ASCE.
History
Published online: Feb 1, 1983
Published in print: Feb 1983
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