This study investigates the flow-mediated interaction between two vibrating cylinders of the same size immersed in an otherwise still fluid. The master cylinder carries out forced vibration, while the slave cylinder is elastically mounted with one degree-of-freedom along the centerline between the two cylinders. We examined the stabilized vibration of the slave cylinder. In total, 6269 two-dimensional (2D) cases were simulated to cover the parameter space, with a fixed Reynolds number of 100, the structural damping factor of the slave cylinder ranging from 0 to 1.4, the mass ratio of the slave cylinder ranging from 1.5 to 2.5, the initial gap ratio ranging from 0.2 to 1.0, the vibration amplitude ratio of the master cylinder ranging from 0.025 to 0.1, and the vibration frequency ratio ranging from 0.05 to 2.4. We found that the vibration amplitude of the slave cylinder is highly sensitive to damping when the damping coefficient is small. The two cylinders' vibration is in antiphase at low frequencies but in phase at high frequencies. The phase of the slave cylinder changes abruptly at resonance when it has little damping, but the phase change with the frequency becomes increasingly gradual with increasing damping. With a nonzero damping factor, the maximum vibration amplitude of the slave cylinder is inversely correlated with its mass ratio. The response of the slave cylinder is explained by examining the pressure distribution and velocity field adjacent to it.

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