Vortex-induced vibration (VIV) of a flexible splitter plate attached to a square cylinder in laminar flow is investigated using fluid–structure interaction (FSI) simulation. The Reynolds number based on the edge length of the square cylinder (L) is fixed at Re $=$ 100, while the structural parameters of the plate are set as ${\rho }_{\mathrm{p}}$ (density ratio) $=$ 84.75, H/L (non-dimensional thickness) $=$ 0.06, E (non-dimensional elastic modulus) $=$ 5$\times 10^3\sim 5\times 10^6$ and l/L (non-dimensional length) $=$ 0.5, 1 and 2, respectively. It is found that the bending rigidity and plate length have significant influences on the dynamic response of the plate, fluid loads on the cylinder–plate body and the vortex pattern in the flow field. At l/L $=$ 0.5, the natural frequency of the plate does not intersect with the vortex shedding frequency in the parameter range considered; VIV of the flexible plate is negligible, and the fluid loads and flow pattern are similar to those in the case of a rigid plate. At l/L $=$ 1, lock-in occurs when the first natural frequency approaches the vortex shedding frequency. In the lock-in regime, the vibrating frequency of the plate shifts to be commensurate with the first natural frequency, and the first-mode bending motion of large amplitude is observed, resulting in higher vortex shedding frequency and narrower vortex street in the wake. At l/L $=$ 2, besides the first-natural-frequency lock-in, the off-centerline phenomenon and second-natural-frequency lock-in are also observed at low elastic modulus. In the off-centerline regime, the mean deflection of the splitter plate shifts to one side and a second-mode-like bending motion appears, which breaks the symmetry of the flow pattern and generates a non-zero mean lift. In the second-natural-frequency lock-in region, the plate vibration and fluid loads are also amplified. The model proposed could be taken as a benchmark for VIV of the flexible plate in laminar flow, and the results obtained are insightful to the design of FSI-based piezoelectric energy harvesters using flexible plates.

使用流固耦合（FSI）仿真研究了层流中附着在方形圆柱体上的柔性隔板的涡激振动（VIV）。基于方柱体（L）的边长的雷诺数固定为Re $=$ 100，而板的结构参数设置为 ${\rho }_{\mathrm{p}}$ （密度比） $=$84.75，H / L  （无量纲的厚度）$=$0.06，E  （无量纲弹性模量）$=$ 5$\times \mathrm{1个}{0}^3〜5\times \mathrm{1个}{0}^6$和l / L  （无量纲长度）$=$分别为0.5、1和2。研究发现，弯曲刚度和板长对板的动力响应，圆柱板体上的流体载荷以及流场中的涡旋模式有重大影响。在L / L $=$0.5，板的固有频率在所考虑的参数范围内与涡旋脱落频率不相交；柔性板的VIV可以忽略不计，流体载荷和流动方式与刚性板类似。在L / L $=$如图1所示，当第一固有频率接近涡旋脱落频率时发生锁定。在锁定状态下，板的振动频率与第一固有频率相称，并且观察到大振幅的第一模式弯曲运动，从而导致较高的涡旋脱落频率和较窄的涡流道。在L / L $=$如图2所示，除了第一固有频率锁定之外，在低弹性模量下也观察到偏心现象和第二固有频率锁定。在偏心状态下，分隔板的平均挠度向一侧移动，出现第二种模式的弯曲运动，这破坏了流型的对称性并产生了非零的平均升程。在第二固有频率锁定区域中，板振动和流体载荷也被放大。所提出的模型可以作为层流中柔性板VIV的基准，所获得的结果对于使用柔性板设计基于FSI的压电能量收集器具有深刻的见解。