A new model for suspension bridges involving the convexification of the cables

TL;DR

This paper introduces a novel suspension bridge model incorporating cable convexification, which predicts earlier torsional instability and simplifies the system by reducing degrees of freedom, offering a more realistic and efficient analysis.

Contribution

It proposes a new model with convexified cables that better reflects real cable behavior and reduces complexity by decreasing the degrees of freedom.

Findings

Convexification of cables predicts lower energy thresholds for torsional instability.

The model simplifies analysis by reducing degrees of freedom to two.

The energy functional involving convexification is complex but manageable with calculus of variations.

Abstract

The final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the behavior of real cables, this model appears more reliable than the classical ones. Moreover, it has the advantage to reduce to two the number of degrees of freedom (DOF), avoiding to introduce the slackening mechanism of the hangers. The drawback is that the resulting energy functional is extremely complicated, involving the convexification of unknown functions. This paper is divided in two main parts. The first part is devoted to the study of these functionals, through classical methods of calculus of variations. The second part applies this study to the suspension bridge model with convexified cables.