The fluid-structure interaction mechanism of flow past multiple structures in proximity is complex. Depending on the initial spacing between a pair of circular cylinders and the reduced flow velocity parameter, the downstream cylinder may undergo wake-induced vibration (WIV) and/or vortex-induced vibration (VIV). This study presents an advanced numerical time-domain simulation model to predict a two-degree-of-freedom WIV, combined with VIV response, of an elastically mounted rigid circular cylinder behind a stationary cylinder in staggered arrangements. The wake deficit flow is modelled based on the boundary layer theory, whereas the unsteady drag and lift hydrodynamic forces due to the vortex shedding of the downstream cylinder are modelled by using the nonlinear van der Pol wake oscillators. The proposed numerical prediction model is calibrated and compared versus experimental data in the literature. For the initial longitudinal centre-to-centre spacing of 4 diameters and the initial transverse spacing of less than 2 diameters, the downstream cylinder first behaves as an isolated cylinder undergoing VIV at a low deficit flow velocity. With increasing flow velocity and Reynolds number, the downstream cylinder exhibits WIV response with progressively increasing oscillation amplitudes in both cross-flow and in-line directions. For staggered cylinders, the time-varying feature of the mean lift force, directed towards the wake centreline and acting on the downstream cylinder, becomes locally asymmetric through the course of the cylinder motion trajectories. This feature modifies WIV response frequencies and leads to an asymmetric trajectory of the cylinder’s two-directional displacements.

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