Mode-by-mode VIVs and 2D-to-3D conversion coefficients of a suspension bridge based on nonlinear energy-trapping properties

3-dimensional (3D) vortex-induced vibrations (VIVs) of a long-span suspension bridge and 2D-to-3D conversion coefficients are addressed in this study. Nonlinear energy-trapping properties (ETPs) represented by van der Pol-type vortex-induced force (VIF) models are realized through model parameters dependent on the motion amplitude, which is based on growth-to-resonance (GTR) VIV evolutions obtained from 2D sectional model tests. Motion-amplitude-dependent (MAD) VIF models are applied to 3D modal shapes to take into account ETPs distributed nonlinearly along the bridge deck. MAD VIF models turn out to be not only able to reconstruct entire GTR processes of a 2D sectional model, but also enable a fast mode-by-mode analysis of 3D full-bridge response. Using a suspension bridge as an example, the nonlinear aerodynamic parameters are determined, on the basis of which ETPs and full-bridge responses are performed. The results show that the nonlinear parameter \(\varepsilon ({U}_{r}, {y}_{T})\) $\epsilon (U_r,y_T)$ has been well identified to reconstruct the GTR curves agreed perfectly with the tested results. The calculated VIV results of the prototype 3D deck vary slightly among different modal shapes with close equivalent mass properties, but vary drastically among those differ obviously in equivalent mass values. VIV conversion coefficients based on MAD models differ significantly from those advised by standards and published literature.