<![CDATA[Flow-Induced Vibration (FIV) in oscillatory flow represents a complex fluid–structure interaction that remains insufficiently explored, particularly for two-degree-of-freedom (2-DoF) systems allowing coupled inline and cross-flow motion. Previous studies have primarily focused on steady flows or limited parameter ranges, leaving a significant knowledge gap in understanding dynamic responses influenced by both reduced velocity ( ) and Keulegan–Carpenter (KC) numbers. This study aims to numerically investigate the vibration characteristics of a 2-DoF circular cylinder subjected to oscillatory flow, emphasizing the coupling mechanism between the two motion directions under varying and KC values. The research employed a numerical approach based on the Direct Forcing Immersed Boundary (DFIB) method integrated with Navier–Stokes solvers and structural motion equations. Simulations were conducted for KC values of 5–20 and ranges between 5–35. The temporal integration was performed using the third-order Adams–Bashforth schemes to ensure accuracy and stability. The results reveal that lock-in phenomena occur within specific UR ranges for each KC value, with resonance peaks identified at = 5 for KC = 5, = 10 for KC = 10, = 15 for KC = 15, and = 20 for KC = 20. Increasing KC values amplify the interaction between flow and structural responses, producing multi-mode vibrations and nonlinear coupling between inline and transverse motions. Furthermore, galloping phenomena were detected at higher UR, indicating a transition from vortex-induced vibration to hydrodynamic instability. These findings contribute to a deeper understanding of FIV dynamics in oscillatory environments, offering insights for optimizing offshore structure design and wave energy harvesting devices.]]>
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