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Inspired by the Melan equation we propose a model for suspension bridges withtwo cables linked to a deck, through inextensible hangers. We write the energyof the system and we derive from variational principles two nonlinear andnonlocal hyperbolic partial differential equations, involving the verticaldisplacement and the torsional rotation of the deck. We prove existence anduniqueness of a weak solution and we perform some numerical experiments on theisolated system; moreover we propose a sensitivity analysis of the system bymechanical parameters in terms of torsional instability. Our results displaythat there are specific thresholds of torsional instability with respect to theinitial amplitude of the longitudinal mode excited.

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