Modal analysis and wake instability analysis on free vibration and prescribed motion of a square cylinder

This study performs fluid-structure interaction numerical simulations (free vibration) of a square cylinder at a Reynolds number of 200 and a mass ratio of 1, varying damping ratios. The vibration amplitude and frequency from the free vibration simulations are used as input for prescribed motion simulations. By comparing the aerodynamic force coefficients and flow fields, the study examines the differences between free vibration and prescribed motion. Higher-Order Dynamic Mode Decomposition is employed to analyze flow characteristics and mode variations, while Floquet stability analysis explores the three-dimensional instability of the wakes in both cases. The results show that prescribed motion closely follows the input parameters, producing a “perfect” result, whereas free vibration is influenced by multiple factors, leading to significant differences in aerodynamic force coefficients, wake patterns, coherent modes, and three-dimensional instability. Additionally, the study finds that small spanwise perturbations of specific wavelengths can disrupt the vortex structures in the flow field, potentially providing a new approach for vibration control of bluff bodies.