Using A Gradient Vector To Find Multiple Periodic Oscillatio

Using a Gradient Vector to Find Multiple Periodic Oscillations in Suspension Bridge
Author(s): L. D. Humphreys and P. J. McKenna

The College Mathematics Journal, Vol. 36, No. 1 (Jan., 2005), pp. 16-26

Published by: Mathematical Association of America

Stable URL:

Tag: Nonlinear differential equations, numerical methods for differential equations

Abstract: The authors explore the forces on suspension bridges such as the Tacoma Narrows Bridge, which collapsed in 1940. The phenomenon of resonance was responsible for the collapse of the Broughton suspension bridge near Manchester, England in 1831. The collapse occurred when a column of soldiers marched in cadence over the bridge, setting up a periodic force of rather large amplitude. For a long time, the collapse of the Tacoma Narrows Bridge was attributed to resonance; however, the authors provide a nonlinear model that better explains the wild vertical and torsional oscillations of the bridge. To find a numerical solution to the model, the authors compare Newton’s method with the method of steepest descent, both of which are accessible to undergraduates.

Review by Thomas W. Judson, Stephen F. Austin State University, March 16, 2013.

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