In this paper, the two-degree-of-freedom (2DOF) vortex-induced vibration (VIV) of a circular cylinder in shear-thinning and shear-thickening non-Newtonian power-law fluids are numerically investigated. A virtual spring-damper-mass system is employed to predict the VIV of the cylinder. A comprehensive analysis is conducted to study the influence of dimensionless parameters, including reduced velocity ($3\le U_r\le 12$) and power-law index ($0.4\le n\le 1.8$) at a low Reynolds number ($Re=150$) and low mass ratio ($m_r=2$) on the vortex shedding pattern, displacement frequencies, local apparent viscosity, friction coefficient, trajectories of the displacements, drag and lift coefficients, and the cylinder displacements. The results indicate that the apparent viscosity and the natural frequency of the system have a substantial effect on the characteristics of the VIV of the cylinder. By changing the values of the reduced velocity, various vortex shedding patterns such as 2S, 2P, S + P, and complex modes are observed for the non- Newtonian fluids, and several motion trajectories other than the typical figure “8″ are analyzed. By increasing the power-law index, the range of the lock-in region and the corresponding reduced velocity of the maximum transverse vibration amplitude change.

本文对非稀疏牛顿幂律流体中剪切稀化和剪切稠化的圆柱体的二自由度（2DOF）涡激振动（VIV）进行了数值研究。虚拟弹簧阻尼器质量系统用于预测气缸的VIV。进行了综合分析以研究无量纲参数的影响，包括降低的速度（$3\le {ü}_{\mathrm{[R}}\le 12$）和幂律指数（$0.4\le ñ\le 1.8$）在低雷诺数（$\mathrm{[R}Ë=150$）和低质量比（${米}_{\mathrm{[R}}=\mathrm{2个}$）上的涡旋脱落模式，位移频率，局部表观粘度，摩擦系数，位移轨迹，阻力和升力系数以及气缸位移。结果表明，系统的表观粘度和固有频率对气缸的VIV特性有很大影响。通过更改降低的速度值，可以观察到非牛顿流体的各种涡旋脱落模式（例如2S，2P，S  +  P和复杂模式），并分析了除典型图形“ 8”以外的几种运动轨迹。通过增大幂律指数，可以改变锁定区域的范围以及最大横向振动幅度相应减小的速度。