For a pair of elastically mounted circular cylinders in a tandem configuration, the downstream cylinder may experience the wake-induced vibration (WIV) due to the hydrodynamic excitation associated with the wake behind the upstream cylinder. In addition to WIV, the downstream cylinder may also be simultaneously subject to the vortex-induced vibration (VIV) due to the vortex shedding in its own wake. This nonlinear coupled wake-vortex interaction can result in a sustained large-amplitude response depending on the cylinder spacing. In this study, a new nonlinear wake-deficit oscillator model for predicting the combined WIV-VIV responses in the cross-flow direction of the downstream cylinder is presented. While the upstream stationary or oscillating cylinder is placed in a uniform steady flow, the downstream cylinder is subject to a non-uniform unsteady flow with a space–time varying velocity being modified by the wake deficit or shielding effect. The total cross-flow hydrodynamic force on the downstream cylinder is modelled as a combination of the wake-induced transverse force and the combined vortex-induced lift and drag forces. The wake-induced force is approximated using a wake deficit theory based on a linearised boundary layer equation. The vortex-induced force is modelled using the van der Pol oscillator which incorporates the wake-deficit flow velocity, relative flow-cylinder velocities and dynamically staggered positions between the two interfering cylinders. These empirical hydrodynamic force equations are nonlinearly coupled, simulating the wake-vortex interaction leading to the combined WIV-VIV responses depending on the fluid–structure parameters. By focusing on the wake interference regime, the wake profiles and hydrodynamic forces are calibrated and validated, introducing new empirical coefficients and functions. The downstream cylinder responses and oscillation frequencies are predicted and compared with relevant experimental data by accounting for the important effects of cylinder spacing ratio, reduced flow velocity and Reynolds number in a subcritical flow regime. The wake stiffness characterisation is also presented, providing an analytical formulation related to the dynamic wake profile. Several key features associated with WIV response amplitudes and frequencies are highlighted and discussed using the calibrated wake-deficit oscillator. The present concept and model can be further improved to account for the effects of in-line response and arbitrarily staggered arrangement as well as the application of multiple long flexible cylinders with multi modal responses.

对于串联配置的一对弹性安装圆柱体，由于与上游圆柱体后面的尾流相关的流体动力激励，下游圆柱体可能会经历尾流引起的振动 (WIV)。除了 WIV 之外，下游圆柱体也可能同时受到涡激振动 (VIV) 的影响，因为涡旋在其尾流中脱落。这种非线性耦合的尾涡相互作用会导致持续的大振幅响应，具体取决于圆柱体间距。在这项研究中，提出了一种新的非线性尾流赤字振荡器模型，用于预测下游气缸横向流动方向上的 WIV-VIV 组合响应。当上游的静止或摆动气缸处于均匀稳定的流动中时，下游圆柱体受到非均匀非定常流动的影响，时空变化速度被尾流不足或屏蔽效应改变。下游圆柱体上的总横向流动水动力被建模为尾流引起的横向力和涡流引起的升力和阻力的组合。尾流诱导力使用基于线性边界层方程的尾流赤字理论来近似。涡流诱导力使用 van der Pol 振荡器建模，该振荡器结合了尾流缺陷流速、相对流动圆柱体速度和两个干涉圆柱体之间的动态交错位置。这些经验水动力方程是非线性耦合的，根据流固参数模拟尾流-涡流相互作用，导致组合 WIV-VIV 响应。通过关注尾流干扰机制，校准和验证尾流剖面和水动力，引入新的经验系数和函数。通过考虑亚临界流态中汽缸间距比、流速降低和雷诺数的重要影响，预测下游汽缸响应和振荡频率并与相关实验数据进行比较。还介绍了尾流刚度特性，提供了与动态尾流剖面相关的分析公式。使用校准的唤醒缺陷振荡器突出并讨论了与 WIV 响应幅度和频率相关的几个关键特征。