Time-variant self-excited force model based on 2D rational function approximation

Large-scale atmospheric turbulence produces large-amplitude low-frequency fluctuations of the angle of attack, which can significantly change the self-excited forces acting on a bridge deck. Such a nonlinear effect must be carefully modelled for an accurate prediction of the dynamic response of long-span suspension bridges to the turbulent wind. By assuming that the angle of attack varies slowly, a time-variant linear model relying on Roger?s rational function approximation (RFA) of the force transfer function is proposed, and a formulation of the problem in the state space is outlined. In particular, an existing model is improved by a flexible fitting of the RFA directly in the multivariate space of reduced velocity and angle of attack. Another contribution of the present work is the setup of an experimental procedure based on bi- or multi-harmonic forced-vibration tests to underscore the variation of magnitude and phase of self-excited forces under a time-variant angle of attack. These wind tunnel tests also allowed a sound experimental validation of the proposed model, considering two quite different bridge deck cross-sections as case studies. Aerodynamic derivatives for various angles of attack were measured to determine the parameters of the model. Despite its simplicity, the model yields accurate results up to relatively fast variations of the angle of attack, and it can reproduce the complicated behaviour of the self-excited forces revealed by the experiments. The performance of the model strongly depends on the goodness of the RFA-based fitting of aerodynamic derivatives, and the excellent results obtained were possible thanks to the high flexibility of the proposed method.