Mathematical Models for Suspension Bridges (G. Arioli, F. Gazzola, C. Marchionna)

Suspension bridges under the action of wind and pedestrian bridges under the synchronised wobble of the pedestrians are subject to vibrations and oscillations. The mathematical modeling of these phenomena is still rather poor, mostly due to the challenge of finding relatively simple models for complicated structures. In order to predict the behavior of bridges and to improve their stability one  needs a careful modeling of elasticity, fluid mechanics, and nonlinear structural mechanics. This demands several interdisciplinary tools: classical methods from ODE’s and PDE’s, analysis of traveling waves, stability techniques from the Floquet theory, shape optimization, minimization of eigenvalues, numerical methods, computer assisted proofs. This topic involves multiple research lines such as:

- to find fully reliable models able to describe qualitatively and quantitatively the structural and the aeroelastic behaviors of suspension and pedestrian bridges, and to compute their thresholds of stability;

- qualitative and quantitative analysis of fourth order ODE’s and PDE’s;

- to find designs able to reduce the oscillations of bridges and to lower the manufacturing costs;

- to numerically and experimentally validate the models, also through a sensitivity analysis;

- analysis of the oscillations through the study of the fluid-structure interaction in suspension bridges and the humans-structure interaction in pedestrian bridges.