Аннотация:
In this talk, we will demonstrate that introducing a convexity constraint on the cables of a suspension bridge causes torsional instability of the deck to emerge at lower energy thresholds. Since this constraint reflects the actual behavior of real cables, the resulting model is more realistic than classical ones. Additionally, it simplifies the system by reducing the number of degrees of freedom to two, eliminating the need to explicitly model the slackening of the hangers.
The main challenge, however, lies in the complexity of the resulting energy functional, which involves the convexification of unknown functions.
We will show how classical tools from the calculus of variations can be used to analyze these non-standard functionals. Finally, we will apply this framework to a suspension bridge model with convexified cables.
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