Abstract The effect of a viscoelastic-type structural support on vortex-induced vibration (VIV) of a circular cylinder has been studied computationally for a fixed mass ratio ( m ∗ = 2 . 546 ) and Reynolds number ( R e = 150 ). Unlike the classical case of VIV where the structural support consists of a spring and damper in parallel, this study considers two springs and one damper, where the two springs are in parallel and the damper is in series with one of the springs. This spring/damper arrangement is similar to the Standard Linear Solid (SLS) model used for modelling viscoelastic behaviour. The viscoelastic support (SLS type) is governed by the following two parameters: (a) the ratio of spring constants ( R ), and (b) the damping ratio ( ζ ). The focus of the present study is to examine and understand the varied response of the cylinder to VIV as these parameters are varied. For small ζ and R , the cylinder response shows characteristics similar to the classical case, where the amplitude response is composed of an upper- and the lower-type branch. The presence of upper-type branch at low R e is evident through the peak lift force, frequency and phase response of the cylinder. As the damping ratio is increased, the vibration amplitude decreases and hence the upper-type branch disappears. There exists a critical value of ζ = 1 beyond which the amplitude again increases asymptotically. The non-monotonic variation of amplitude response with ζ is presented in the form of the ”Griffin plot”. The amplitude, force, frequency and phase-difference response of cylinder were found to be mirror symmetric in log ( ζ ) about ζ = 1 . In addition, the effect of R at the critical value of damping, ζ = 1 , was studied. This show that the amplitude decreases with an increase of R , with suppression of the response branches for high R values. The results suggest that a careful tuning of the damping may be effectively employed both to enhance power output for energy extraction applications or to suppress flow-induced vibration.

中文翻译：

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低雷诺数下粘弹性支撑上圆柱体的横向涡激振动

摘要 在固定质量比 ( m ∗ = 2 . 546 ) 和雷诺数 ( Re = 150 ) 下，粘弹性型结构支撑对圆柱涡激振动 (VIV) 的影响进行了计算研究。与结构支撑由平行的弹簧和阻尼器组成的经典 VIV 情况不同，本研究考虑了两个弹簧和一个阻尼器，其中两个弹簧平行且阻尼器与其中一个弹簧串联。这种弹簧/阻尼器布置类似于用于模拟粘弹性行为的标准线性实体 (SLS) 模型。粘弹性支撑（SLS 类型）由以下两个参数控制：(a) 弹簧常数比 (R)，和 (b) 阻尼比 (ζ)。本研究的重点是检查和理解气缸对 VIV 的不同响应，因为这些参数是变化的。对于小的 ζ 和 R ，圆柱响应表现出类似于经典情况的特征，其中幅度响应由上型和下型分支组成。通过气缸的峰值升力、频率和相位响应，可以明显看出在低 Re e 时存在上型分支。随着阻尼比的增加，振幅减小，因此上型分支消失。存在 ζ = 1 的临界值，超过该值振幅再次渐近增加。振幅响应随 ζ 的非单调变化以“格里芬图”的形式呈现。振幅、力、发现圆柱的频率和相位差响应在 log ( ζ ) 上是镜像对称的，大约 ζ = 1 。此外，还研究了 R 对阻尼临界值 ζ = 1 的影响。这表明幅度随着 R 的增加而减小，同时抑制了高 R 值的响应分支。结果表明，仔细调整阻尼可以有效地提高能量提取应用的功率输出或抑制流动引起的振动。