Vortex-induced vibrations and galloping of a square cylinder: The impact of damping and mass ratio

This paper focuses on the effects of the damping ratio and mass ratio on the vortex-induced vibration (VIV) and galloping of a square cylinder through numerical simulations at a Reynolds number 200. Dynamic Mode Decomposition (DMD) is applied to uncover how the damping ratio influences the vortex shedding mode of the cylinder. The results show that for VIV, the vibration amplitude decreases with an increasing damping ratio as is expected, and the corresponding mathematic model is provided. As the damping ratio increases, the mean drag coefficient decreases, while the standard deviation of the fluctuating lift coefficient decreases rapidly before gradually rising, with a knee point at damping ratio 0.23. With increasing damping ratio, the dominant mode changes while the vortex shedding mode remains “2S”. For galloping, the mean drags, vibration amplitude, and fluctuating lift all decrease sharply with rising damping ratio, after which they stabilize. The mathematic model for vibration amplitude and damping ratio is also provided. This inflection point is identified as the critical damping ratio, which regulates the onset of galloping. Across this process, the dominant mode remains M1, while the vortex shedding mode transitions from “P + S” to “2S” as the damping ratio increases.