Vortex-induced vibration of bridge decks: Describing function-based model

A describing function (DF)-based model is introduced for the simulation of vortex-induced vibration (VIV) of bridge decks. Similar to the linear frequency response function, the DF is the complex ratio of the first-order component of the nonlinear output to the harmonic input. The DF can be either identified using the forced vibration technique or based on the VIV nonlinear response time history. An iterative procedure is accordingly developed to predict the VIV response with the DF-based model, and an equivalent-damping-ratio-based simplified method is further proposed to efficiently obtain the limit cycle oscillation (LCO) amplitude of VIV. It is demonstrated that the conventional van der Pol-type model is equivalent to a special case of the DF-based model for VIV. Three case studies involving various cross-sections are utilized to validate the simulation accuracy and efficiency of the proposed DF-based model for typical features at VIV lock-in such as LCO and hysteresis phenomena. The vertical VIVs can be well captured by the DF-based model, while its capability of simulating the torsional VIVs requires further improvement. Furthermore, the predictive capability of DF-based model for vertical VIVs of bridge decks within a wide range of mass-damping conditions is highlighted.