Enhanced linearized flutter analysis of suspension bridges

We investigate the dynamic stability of a single-span suspension bridge deck, subjected to a uniform transverse wind, through a linearized continuous model. The deck, modelled as an elastic beam of constant cross-section, inextensible and unshearable though deformable in bending and torsion, is connected to the main cables by a continuous system of rigid suspenders; both primary (i.e., Saint Venant) and secondary (i.e., Vlasov) torsional rigidities are taken into account. The integro-differential equations governing the dynamic equilibrium of the deck are derived at first by considering the steady wind component (mean wind). Two separate solutions are obtained, by the Galerkin method, for the antisymmetric and symmetric oscillations, giving the natural frequencies as functions of the aerodynamic loads. Afterwards, dynamic stability (i.e., flutter) is studied by including the unsteady aerodynamic loads in the equations of motion.