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, 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.

本文的最终目的是表明，通过在悬索桥的电缆上插入凸度约束，在较低的能量阈值处出现甲板的扭转不稳定性。由于实际电缆的行为暗示了这一约束，因此该模型似乎比经典电缆更可靠。此外，具有将自由度减少至两个的优点，避免引入衣架的松弛机构。缺点是生成的能量函数极其复杂，涉及未知函数的凸化。本文分为两个主要部分。第一部分致力于通过经典的微积分方法研究这些功能。第二部分将本研究应用于凸电缆悬索桥模型。