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Large Torsional Oscillations in Suspension Bridges Visited Again: Vertical Forcing Creates Torsional Response
by P. J. McKenna (University of Connecticut ) and Cillian Ó Tuama (University College Cork, Ireland)
This article originally appeared in:American Mathematical Monthly
October, 2001
Subject classification(s): Mathematical Physics | Applied Mathematics | Nonlinear Oscillations | Second Order Ordinary Differential Equations | Ordinary Differential Equations | Differential and Difference Equations | Numerical Analysis | Analysis
Applicable Course(s): 4.17 Numerical Analysis | 4.15 Advanced Differential Equations | 3.6 Differential Equations
This article is part of the Mathematics of Planet Earth 2013 Collection. This article follows up on an earlier paper by the first author discussing a model that predicts the behavior of the Tacoma Narrows Bridge just before collapse. The authors discuss a model with two linked nonlinear second-order ordinary differential equations. One equation models the torsion of the bridge and the other the vertical displacement from equilibrium. The authors’ main point in this paper is that, “[H]igh frequency vertical forcing can result in a periodic motion that is predominantly torsional.” The solution of these equations is numerical. The authors encourage undergraduates to experiment with various initial conditions. See also the earlier paper by McKenna on this subject.
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