Numerical simulation of windless-air-induced added mass and damping of vibrating bridge decks

Abstract

The windless-air-induced added mass/mass moment of inertia (ma/Ia) and damping (ca) effects on mechanical parameters of a vibrating bridge deck are usually ignored in wind tunnel tests. In this paper, for three typical deck sections, computational fluid dynamics simulations are carried out to study the vertical/torsional single degree-of-freedom forced vibration under windless conditions, and further to reveal the effects of ma, Ia, and ca on the modal parameters. The influences of turbulence model, computational domain size, grid resolution, and time step size are analyzed. For the addressed issue, the Reynolds stress equation model (RSM) is found to be more suitable than the shear stress transportation (SST) k-ω model. A mathematical model for aerodynamic forces at zero wind speed is presented by using the dimensionless ma, Ia, and ca, and they can be extracted by combining the motions and the numerically simulated aerodynamic forces using the least squares method. The numerically simulated results for an ideal plate under small amplitudes are very close to the theoretical values, and consequently verify their accuracy. The causes for the non-zero values of flutter derivatives H4∗ and A3∗ at zero wind speed are revealed. In the windless air, the added damping almost linearly increases with the vibration amplitude. Five existing long-span bridge deck models are taken as examples to investigate the effects of ma, Ia, and ca on structural frequencies and damping ratios.