  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.
