Geodesic
Nonlinearity in oscillating bridges
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 74B20, 35G31, 34C15, 74K10, 74K20
Keywords: suspension bridges, nonlinear elasticity 
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     author = {Gazzola, Filippo},
     title = {Nonlinearity in oscillating bridges},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a166/}
}
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Gazzola, Filippo. Nonlinearity in oscillating bridges. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a166/