Torsional instability and sensitivity analysis in a suspension bridge model related to the Melan equation

TL;DR

This paper develops a nonlinear hyperbolic PDE model for suspension bridges based on the Melan equation, analyzing torsional instability and sensitivity to parameters through theoretical and numerical methods.

Contribution

It introduces a new mathematical model for suspension bridges incorporating torsional effects and provides a sensitivity analysis of torsional instability thresholds.

Findings

Existence and uniqueness of weak solutions established.

Numerical experiments illustrate torsional instability thresholds.

Sensitivity analysis identifies critical parameters affecting stability.

Abstract

Inspired by the Melan equation we propose a model for suspension bridges with two cables linked to a deck, through inextensible hangers. We write the energy of the system and we derive from variational principles two nonlinear and nonlocal hyperbolic partial differential equations, involving the vertical displacement and the torsional rotation of the deck. We prove existence and uniqueness of a weak solution and we perform some numerical experiments on the isolated system; moreover we propose a sensitivity analysis of the system by mechanical parameters in terms of torsional instability. Our results display that there are specific thresholds of torsional instability with respect to the initial amplitude of the longitudinal mode excited.