Van der Pol-type equation for modeling vortex-induced oscillations of bridge decks

A careful modeling of vortex-induced vibration of a bridge deck allows to avoid fatigue damages and the reduction of travel safety and/or comfort levels for the users. The existing empirical models do not seem to be fully reliable because they are not able to predict the response oscillation amplitude for values of the mass and damping away from those at which their aeroelastic parameters were estimated. A van der Pol-type equation is used in the Ehsan–Scanlan's model, which for practical reasons seems to be the more suitable model for vortex-induced vibration of bridge decks. In this work this model was deeply studied and wind-tunnel tests on a 4:1 rectangular cylinder were performed to apply it to a realistic case study. Numerical integrations of the van der Pol-type equation highlighted its physical coherence to model vortex-induced vibrations of structures prone to the wind action. Moreover, it was verified that the assumptions standing behind the Ehsan–Scanlan's identification procedure of the aeroelastic parameters are justified. Finally, an alternative identification procedure was proposed, consisting in a numerical estimation of the aeroelastic parameters directly from the nonlinear differential equation.