Resonance forever: existence of a critical mass and an infinite regime of resonance in vortex-induced vibration
Resonance forever: existence of a critical mass and an infinite regime of resonance in vortex-induced vibration
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DOI：
10.1017/s0022112002002318
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发表时间：
2002-12
影响因子：
3.7
通讯作者：
R. N. Govardhan;C. Williamson
中科院分区：
文献类型：
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作者：
R. N. Govardhan;C. Williamson
本文研究了无结构恢复力（k = 0）圆柱的横向涡激振动。就常规使用的归一化流速U* 而言，本实验对应于无限值（其中U* = U/fND，fN =固有频率，D =直径）。将质量比m*（质量/位移质量）从经典研究的m* = 100级的值降低到m* = 1，产生的振荡可以忽略不计。然而，质量的进一步减少表现出令人惊讶的结果：大振幅剧烈振动突然出现的质量值小于临界质量比，m* 临界= 0.54。自den Hartog（1934）的工作以来，经典的假设是共振大振幅振荡只存在于一个很窄的速度范围内，大约U* 105，在这个速度范围内，旋涡脱落频率与自然频率相当。然而，在本研究中，我们证明，只要身体的质量低于这个临界值，共振振荡的归一化速度（U*）的制度是无限宽的，从U* → 5开始，并延伸到U*→∞。这一结果与Govardhan和威廉姆森（2000）基于弹性安装振动研究（k > 0）提出的预测完全一致。我们推导出一个条件下，这种不寻常的概念的一个无限宽的制度的共振将发生在任何通用的涡激振动系统。
In this paper, we study the transverse vortex-induced vibrations of a cylinder with no structural restoring force (k = 0). In terms of the conventionally used normalized flow velocity, U*, the present experiments correspond to an infinite value (where U* = U/fND, fN = natural frequency, D = diameter). A reduction of mass ratios m* (mass/displaced mass) from the classically studied values of order m* = 100, down to m* = 1, yields negligible oscillations. However, a further reduction in mass exhibits a surprising result: large-amplitude vigorous vibrations suddenly appear for values of mass less than a critical mass ratio, m*crit = 0.54. The classical assumption, since the work of den Hartog (1934), has been that resonant large-amplitude oscillations exist only over a narrow range of velocities, around U*∼5, where the vortex shedding frequency is comparable with the natural frequency. However, in the present study, we demonstrate that, so long as the body’s mass is below this critical value, the regime of normalized velocities (U*) for resonant oscillations is infinitely wide, beginning at around U*∼5 and extending to U*→∞. This result is in precise accordance with the predictions put forward by Govardhan & Williamson (2000), based on elastically mounted vibration studies (where k > 0). We deduce a condition under which this unusual concept of an infinitely wide regime of resonance will occur in any generic vortex-induced vibration system.