Nonlinearity in oscillating bridges

TL;DR

This paper reviews historical and recent oscillating bridges, critiques existing models, and advocates for revisiting classical theories to develop more reliable models that accurately capture self-excited oscillations.

Contribution

It highlights the need to revise classical models of oscillating bridges and proposes new modeling approaches to better understand and predict their behavior.

Findings

Classical models often rely on linear elasticity, which is inadequate for large oscillations.

Recent models show solutions with self-excited oscillations matching real bridge behavior.

A call for revisiting and improving existing models to enhance reliability.

Abstract

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 strongly 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 classical models, to introduce reliable models, and to indicate the steps we believe necessary to reach this target.