Flow-induced vibrations of a square cylinder at different angles of attack: The importance of the in-line vibrations

A square cylinder is an ideal geometry for investigating both vortex-induced vibration (VIV) and galloping instabilities. The present work aims to evaluate the significance of in-line freedom on the flow-induced vibrations (FIVs) of a square cylinder subjected to flow. Numerical simulations were conducted for both a two-degree-of-freedom (2-DOF) and a one-degree-of-freedom (1-DOF) square cylinder with different angles of attack. The mass ratio, which is the structural mass divided by the displaced fluid mass, is set to 5, and the Reynolds number is fixed at 200. Detailed comparisons of the amplitude responses, frequency responses, hydrodynamic characteristics, fluid forces, transitions of VIV-galloping, and vortex shedding modes of the 2-DOF cylinder and the one with only cross-flow oscillation were conducted. Overall, the vibration trend of the 1-DOF square cylinder is similar to that of the 2-DOF square cylinder. However, when α is between 5° and 20°, the results show that there are two obvious amplitude peak regions in the vibration response of the 2-DOF square cylinder, while the second amplitude peak region is not found of the 1-DOF square cylinder. This indicates that considering in-line vibrations is crucial for investigating the FIV of a square cylinder, as the in-line freedom can alter the responses of the cross-flow vibrations.