Electron. J. Diff. Equ., Vol. 2013 (2013), No. 211, pp. 1-47.

Nonlinearity in oscillating bridges

Filippo Gazzola

We first recall several historical oscillating bridges that, in some cases, led to collapses. Some of them are quite recent and show that, nowadays, oscillations in suspension bridges are not yet well understood. Next, we survey some attempts to model bridges with differential equations. Although these equations arise from quite different scientific communities, they display some common features. One of them, which we believe to be incorrect, is the acceptance of the linear Hooke law in elasticity. This law should be used only in presence of small deviations from equilibrium, a situation which does not occur in widely oscillating bridges. Then we discuss a couple of recent models whose solutions exhibit self-excited oscillations, the phenomenon visible in real bridges. This suggests a different point of view in modeling equations and gives a strong hint how to modify the existing models in order to obtain a reliable theory. The purpose of this paper is precisely to highlight the necessity of revisiting the classical models, to introduce reliable models, and to indicate the steps we believe necessary to reach this target.

Submitted June 10, 2013. Published September 20, 2013.
Math Subject Classifications: 74B20, 35G31, 34C15, 74K10, 74K20.
Key Words: Suspension bridges; nonlinear elasticity.

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Filippo Gazzola
Dipartimento di Matematica del Politecnico
Piazza L. da Vinci 32 - 20133 Milano, Italy
email: filippo.gazzola@polimi.it

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