The vortex-induced vibration (VIV) of circular cylinder in uniform flow with two-degree-of-freedom (2DOF) and geometrical nonlinear system is investigated numerically using the combined sliding and layering dynamic meshes. The characteristics of vibration amplitude, fluid force coefficients, branching behaviour, vibration trajectory, energy transfer and flow pattern of circular cylinder in VIV are studied with two-dimensional shear stress transfer (SST) $k$-$\omega$ turbulence model and three-dimensional large eddy simulation (LES). It is found that in the simulation with LES model the predicted vibration amplitude and fluid force coefficients show good agreement with the experimental data, while in the simulation with SST $k$-$\omega$ model these parameters are significantly underestimated. The two triplets (2T) vortex shedding mode happens in the super upper branch of circular cylinder with 2DOF linear system and leads the large-magnitude positive energy transferring from fluid to cylinder, which causes the maximum vibration amplitude. For the circular cylinder with 2DOF nonlinear system, the vibration simulated by LES model shows a galloping-like phenomenon that the amplitude keeps increasing with the reduced velocity ${\mathit{U}}_r$. The crescent-shaped trajectory and the 2T vortex shedding mode happen upon the critical ${\mathit{U}}_r$, which is similar to that in the super upper branch of circular cylinder with 2DOF linear system. This phenomenon is caused by the amplitude-dependent stiffness of nonlinear system and the modified reduced velocity ${\mathit{U}}^{\mathrm{\ast }}$ reveals the universality of vibration amplitude for the circular cylinders with linear and nonlinear systems.

使用组合滑动和分层动态网格对具有二自由度 (2DOF) 和几何非线性系统的均匀流动中圆柱体的涡激振动 (VIV) 进行了数值研究。利用二维剪切应力传递(SST)研究了VIV中圆柱体的振幅、流体力系数、分支行为、振动轨迹、能量传递和流动模式的特性$克$——$\omega$湍流模型和三维大涡模拟 (LES)。发现在LES模型模拟中，预测的振幅和流体力系数与实验数据吻合良好，而在SST模拟中$克$——$\omega$模型这些参数被严重低估。两个三元组（2T）涡旋脱落模式发生在具有2DOF线性系统的圆柱体的超上分支，并导致从流体到圆柱体的大幅度正能量传递，导致最大振幅。对于具有2DOF非线性系统的圆柱体，LES模型模拟的振动表现出类似飞驰的现象，振幅随着速度的降低而不断增加${\mathit{你}}_r$. 新月形轨迹和 2T 涡旋脱落模式发生在临界${\mathit{你}}_r$，类似于具有2DOF线性系统的圆柱体的超上分支。这种现象是由非线性系统的振幅相关刚度和修正的减速度引起的${\mathit{你}}^{\mathrm{＊}}$ 揭示了具有线性和非线性系统的圆柱体振动幅度的普遍性。