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IMA Journal of Applied Mathematics 2002 67(5):459-478; doi:10.1093/imamat/67.5.459
© 2002 by Institute of Mathematics and its Applications
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The global structure of periodic solutions to a suspension bridge mechanical model

P. J. McKenna1 and K. S. Moore2

1 Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA 2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA

We study two systems of nonlinearly coupled ordinary differential equations that govern the vertical and torsional motions of a cross-section of a suspension bridge. We observe numerically that the structure of the set of periodic solutions changes considerably when we smooth the nonlinear terms. The smoothed nonlinearities describe the force that we wish to model more realistically and the resulting periodic solutions more accurately replicate the phenomena observed at the Tacoma Narrows Bridge on the day of its collapse. The main conclusion is that purely vertical periodic forcing can result in subharmonic primarily torsional motion.

Keywords: torsional oscillations; coupled oscillations; suspension bridge.

Received 6 September 2001.


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