This article investigates flow-induced vibrations (FIV) of structures, which represent one of the critical challenges in hydraulic, mechanical, and civil engineering systems. A comprehensive analysis of fluid–structure interaction was carried out using both experimental investigations and numerical simulations. The study examines vortex shedding mechanisms, resonance phenomena, and the influence of flow parameters on the amplitude and frequency of vibrations in cylindrical structures. Experimental tests were conducted in a hydrodynamic water tunnel using a laser vibrometer and Particle Image Velocimetry (PIV) techniques, while numerical simulations were implemented through a Fluid–Structure Interaction (FSI) framework using OpenFOAM software. The obtained results demonstrate that maximum vibration amplitudes occur within the lock-in regime at a reduced velocity of approximately 6, where synchronization between vortex shedding frequency and the natural frequency of the structure takes place. It was found that increasing the damping ratio reduces vibration amplitudes by up to 25%. A comparison between experimental and numerical results confirmed the high accuracy of the proposed model, with discrepancies below 10%. The findings can be applied in the design of hydraulic structures, pipelines, bridge systems, and offshore engineering facilities to improve their operational reliability and vibration resistance.