Abstract The effect of structural nonlinearity on vortex-induced vibration of a rigid circular cylinder has been studied computationally for a fixed mass ratio of m ∗ = 2 . 546 at R e = 150 . The arrangement of the springs and damper is similar to setup for the Standard Linear Solid (SLS) model used to model a viscoelastic material. One linear spring is in series with the damper and another nonlinear spring is parallel with the damper. The nonlinear structural system is governed by the following three parameters: (a) the ratio of the linear spring constants ( R ), (b) damping ratio ( ζ ), and (c) nonlinearity strength ( λ ). The focus of the present study is to examine the response of the cylinder to VIV by changing ζ and λ . The peak amplitude decreases in comparison with a linear spring, as spring softening ( λ 0 ) is increased; in contrast, the peak amplitude increases for a hardening spring ( λ > 0 ). The equivalent reduced velocity ( U r e q ), a measure of nonlinearity, is affected by damping, showing the non-monotonic variation with ζ . There exists a critical value ζ ≈ 1 below which the equivalent reduced velocity decreases and beyond which U r e q increases. We also observed at high values of λ (e.g. λ = 4 ), the peak lift force coefficient is almost constant over a wide range of reduced velocity, with the absence of the lower branch for a very low ( ζ = 0 . 001 ) and high ( ζ = 10 ) values of damping. This near constant amplitude range suggests a hardening spring may be useful for extending the operational range for energy extraction applications. Finally, increased system nonlinearity leads to considerably richer spectral content in the displacement and force signals, reflected in the wake development.

中文翻译：

---

非线性粘弹性支撑上圆柱体的涡激振动

摘要 结构非线性对刚性圆柱体涡激振动的影响已经在固定质量比 m ∗ = 2 的情况下进行了计算研究。在 Re = 150 时为 546。弹簧和阻尼器的布置类似于用于模拟粘弹性材料的标准线性实体 (SLS) 模型的设置。一个线性弹簧与阻尼器串联，另一个非线性弹簧与阻尼器平行。非线性结构系统由以下三个参数控制：(a) 线性弹簧常数的比率 (R)，(b) 阻尼比 (ζ)，以及 (c) 非线性强度 (λ)。本研究的重点是通过改变 ζ 和 λ 来检查圆柱体对 VIV 的响应。与线性弹簧相比，峰值振幅减小，因为弹簧软化 (λ 0 ) 增加；相比之下，硬化弹簧的峰值振幅增加 (λ > 0)。等效折减速度 (U req ) 是非线性度量，受阻尼影响，显示出与 ζ 的非单调变化。存在一个临界值 ζ ≈ 1，低于该值，等效减小速度会降低，超过该值 U req 会增加。我们还观察到在高 λ 值（例如 λ = 4 ）下，峰值升力系数在很宽的降低速度范围内几乎是恒定的，对于非常低的（ ζ = 0 . 001 ）和没有较低的分支高 ( ζ = 10 ) 阻尼值。这种接近恒定的振幅范围表明硬化弹簧可能有助于扩展能量提取应用的操作范围。最后，增加的系统非线性导致位移和力信号中的频谱内容更加丰富，