Vortex-induced vibrations (VIV) in systems with more than one degree of freedom often present complex synchronization among the motion components, also hidden by the randomness that characterizes the motion itself. A phase average method has been here developed and applied to the displacements of a tethered sphere, at low mass and damping, to analyze its xy trajectories over a wide range of reduced velocities, 5 ≤ U* ≤ 25 (Reynolds numbers, 5.1 × 103 ≤ Re ≤ 2.67 × 104). This method has allowed the identification of both the periodic and chaotic contribution of each motion component, accurately reconstructing the underlying trajectory periodic pattern. The two classical vibration modes, I and II, have been also observed. The method developed here was able to better rebuild the experimental data compared to other methods found in the relevant literature, providing useful insights into the study of the dynamic response of a freely-oscillating tethered sphere immersed in a steady flow.

中文翻译：

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系留球涡激振动的一种分析方法

具有一个以上自由度的系统中的涡激振动 (VIV) 通常会在运动组件之间呈现复杂的同步，也被运动本身的随机性所掩盖。这里开发了一种相位平均方法，并应用于低质量和低阻尼的系留球体的位移，以分析其 xy 轨迹在广泛的降低速度范围内，5 ≤ U* ≤ 25（雷诺数，5.1 × 103 ≤ Re ≤ 2.67 × 104)。这种方法允许识别每个运动分量的周期性和混沌贡献，准确地重建潜在的轨迹周期模式。还观察到了两种经典振动模式 I 和 II。