Aeroelastic stability of long span bridges: comparison between quasi-deterministic and POD-based representation of the wind turbulence

The effects on the aeroelastic stability of long span bridges of low-frequency wind speed fluctuations are addressed. The spatial-temporal field of wind turbulence implies a perturbation of the critical state of the 1dof system (flutter mode) representing the 3D oscillations (vertical, transversal and torsional) of the bridge under a non-turbulent critical windspeed. From a mathematical point of view, the contribution of the wind turbulence introduces parametric excitations, both on the stiffness and on the damping terms of the equation describing the time-evolution of the flutter mode; as a consequence, the turbulence effects can make the critical state unstable, unless the mean wind speed is appropriately lowered with respect to the classical and ideal case (i.e. non-turbulent wind). In this paper, two different descriptions of the spatial-temporal field of wind turbulence are discussed and compared: i) a POD-based representation; ii) a quasi deterministic model of the wind field, underestimating the loss of coherence between different points. It is shown that the reduction of mean wind speed required to assure aeroelastic stability in case of turbulent wind, that can be obtained as a closed form upper bound by means of the representation (ii), is not negligible even for a more realistic wind-turbulence field (i) and for the sample case of an aerodynamically optimized long span bridge.