With the development of offshore oil production and the resulting application of riser pipes, it is necessary to get a better understanding of the flow-induced vibrations (FIV) phenomenon involving multiple cylindrical structures. In this scenario, little is available concerning the phase difference between the transverse displacements of two long rigid cylinders (aspect ratio of 30) in tandem and free to vibrate due to the flow incidence. Aiming to fill this gap, experiments were carried out at the towing tank of the Technological Research Institute (IPT) for two similar rigid cylinders in a tandem arrangement. Both cylinders were elastically supported with two degrees of freedom (2DOF), the in-line and transverse direction. Different tandem distances were tested ( $$T=2D$$ T = 2 D , 2.5 D , 3 D , 4 D and 6 D ) throughout the complete excitation of the lock-in range for the upstream cylinder, i.e., reduced velocities ranged from 3 to 13, which corresponds to Reynolds numbers from $$3\times 10^3$$ 3 × 10 3 to $$3\times 10^4$$ 3 × 10 4 . This work found the upstream cylinder having a qualitatively similar response compared with the isolated one. The downstream cylinder exhibited large response amplitudes compared with the upstream one in the lower branch of vibration. Lastly, the phase difference between transverse displacements of both cylinders was classified according to five phase patterns, two of them apparently related to the initial and upper branches of vibration in all cases.

中文翻译：

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串联配置刚性圆柱体的 2DOF FIV 横向位移相分析

随着海上石油生产的发展以及由此产生的立管的应用，有必要更好地了解涉及多个圆柱结构的流动诱导振动 (FIV) 现象。在这种情况下，关于串联的两个长刚性圆柱（纵横比为 30）的横向位移之间的相位差几乎没有可用的信息，并且由于流动入射而自由振动。为了填补这一空白，在技术研究所 (IPT) 的牵引油箱中对两个类似的刚性油缸串联布置进行了实验。两个圆柱体都由两个自由度 (2DOF) 弹性支撑，即轴向和横向。测试了不同的串联距离（ $$T=2D$$ T = 2 D , 2.5 D , 3 D , 4 D 和 6 D ) 贯穿上游气缸锁定范围的完整激发，即降低的速度范围从 3 到 13，这对应于雷诺数从 $3\times 10^3$$ 3 × 10 3到 $$3\times 10^4$$ 3 × 10 4 。这项工作发现上游圆柱体与孤立圆柱体相比，具有定性相似的响应。在振动的下部分支中，与上游气缸相比，下游气缸表现出较大的响应幅度。最后，两个圆柱体的横向位移之间的相位差根据五种相位模式进行分类，其中两种显然与所有情况下的初始和上部振动分支有关。这对应于雷诺数从 $$3\times 10^3$$ 3 × 10 3 到 $$3\times 10^4$$ 3 × 10 4 。这项工作发现上游圆柱体与孤立圆柱体相比，具有定性相似的响应。在振动的下部分支中，与上游气缸相比，下游气缸表现出较大的响应幅度。最后，两个圆柱体的横向位移之间的相位差根据五种相位模式进行分类，其中两种显然与所有情况下的初始和上部振动分支有关。这对应于雷诺数从 $$3\times 10^3$$ 3 × 10 3 到 $$3\times 10^4$$ 3 × 10 4 。这项工作发现上游圆柱体与孤立圆柱体相比，具有定性相似的响应。在振动的下部分支中，与上游气缸相比，下游气缸表现出较大的响应幅度。最后，两个圆柱体横向位移之间的相位差根据五种相位模式进行分类，其中两种显然与所有情况下的初始和上分支振动有关。