Motion-amplitude-dependent nonlinear VIV model and maximum response over a full-bridge span

Abstract

Nonlinear motion-amplitude $$(y_{T} )$$ -dependent energy-trapping properties of a bridge model undergoing vortex-induced vibration (VIV) are investigated. Energy-trapping properties of the model undergoing a full-process from still to a limit cycle oscillation (LCO) state are identified. A van der Pol-type model is adapted to describe the amplitude-dependent aerodynamic properties. Nonlinear parameter-amplitude relations, $$\varepsilon {-}y_{T}$$ and $$\xi_{\varepsilon } {-}y_{T}$$ , are established. Nonlinear aerodynamic damping is separated into two parts: the initial damping which varies with the reduced wind speed, and the $$\varepsilon $$ -related part which varies with both the reduced wind speed and the motion amplitude. The initial aerodynamic damping determines the threshold of VIV, while the $$\varepsilon $$ -related part dominates the evolution process and the LCO. The identified nonlinear analytical model is capable of predicting VIV responses at higher mechanical damping ratios. The energy-trapping properties of a section model in time are transformed into nonlinear properties distributed in space along an elongated 3-D elastic bridge span. According to this “time-space” transformation, the convection coefficient, which links the maximum response of a 3-D structure with that of a 2-D (1-DOF) sectional model, can be determined. Compared with a constant-parameter analytical model, an adapted nonlinear one brings to light significantly larger convection coefficients. Finally, parameter overflowing phenomena are revealed and discussed.