A nonlinear mathematical model is developed in the time domain to simulate the behaviour of two identical flexibly mounted cylinders in tandem while undergoing vortex-induced vibration (VIV). Subsequently, the model is validated and modified against experimental results. Placing an array of bluff bodies in proximity frequently happens in different engineering fields. Chimney stacks, power transmission lines and oil production risers are few engineering structures that may be impacted by VIV. The coinciding of the vibration frequency with the structure natural frequency could have destructive consequences. The main objective of this study is to provide a symplectic and reliable model capable of capturing the wake interference phenomenon. This study shows the influence of the leading cylinder on the trailing body and attempts to capture the change in added mass and damping coefficients due to the upstream wake. The model is using two coupled equations to simulate the structural response and hydrodynamic force in each of cross-flow and stream-wise directions. Thus, four equations describe the fluid–structure interaction of each cylinder. A Duffing equation describes the structural motion, and the van der Pol wake oscillator defines the hydrodynamic force. The system of equations is solved analytically. Two modification terms are added to the excitation side of the Duffing equation to adjust the hydrodynamic force and incorporate the effect of upstream wake on the trailing cylinder. Both terms are functions of upstream shedding frequency (Strouhal number). Additionally, the added mass modification coefficient is a function of structural acceleration and the damping modification coefficient is a function of velocity. The modification coefficients values are determined by curve fitting to the difference between upstream and downstream wake forces, obtained from experiments. The damping modification coefficient is determined by optimizing the model against the same set of experiments. Values of the coefficients at seven different spacings are used to define a universal function of spacing for each modification coefficient so that they can be obtained for any given distance between two cylinders. The model is capable of capturing lock-in range and maximum amplitude.

在时域中开发了一个非线性数学模型，以模拟两个相同的柔性串联气缸在经受涡激振动 (VIV) 时的行为。随后，根据实验结果验证和修改模型。将一系列钝体靠近放置经常发生在不同的工程领域。烟囱、输电线路和石油生产立管是少数可能受 VIV 影响的工程结构。振动频率与结构固有频率的重合可能会产生破坏性后果。本研究的主要目的是提供一种能够捕捉尾流干扰现象的辛而可靠的模型。这项研究显示了前圆柱体对尾体的影响，并试图捕捉由于上游尾流引起的附加质量和阻尼系数的变化。该模型使用两个耦合方程来模拟结构响应和流体动力在每个横向和流动方向上的力。因此，四个方程描述了每个圆柱体的流固耦合。Duffing 方程描述结构运动，van der Pol 尾流振荡器定义流体动力。方程组被解析求解。两个修正项被添加到 Duffing 方程的激励侧以调整流体动力并结合上游尾流对尾随气缸的影响。这两项都是上游脱落频率（斯特劳哈尔数）的函数。此外，附加质量修正系数是结构加速度的函数，阻尼修正系数是速度的函数。修正系数值是通过曲线拟合上游和下游尾流力之间的差异来确定的，从实验中获得。阻尼修正系数是通过针对同一组实验优化模型来确定的。七个不同间距的系数值用于定义每个修正系数的间距的通用函数，以便可以针对两个圆柱体之间的任何给定距离获得它们。该模型能够捕获锁定范围和最大振幅。修正系数值是通过曲线拟合上游和下游尾流力之间的差异来确定的，从实验中获得。阻尼修正系数是通过针对同一组实验优化模型来确定的。七个不同间距的系数值用于定义每个修正系数的间距的通用函数，以便可以针对两个圆柱体之间的任何给定距离获得它们。该模型能够捕获锁定范围和最大振幅。修正系数值是通过曲线拟合上游和下游尾流力之间的差异来确定的，从实验中获得。阻尼修正系数是通过针对同一组实验优化模型来确定的。七个不同间距的系数值用于定义每个修正系数的间距的通用函数，以便可以针对两个圆柱体之间的任何给定距离获得它们。该模型能够捕获锁定范围和最大振幅。七个不同间距的系数值用于定义每个修正系数的间距的通用函数，以便可以针对两个圆柱体之间的任何给定距离获得它们。该模型能够捕获锁定范围和最大振幅。七个不同间距的系数值用于定义每个修正系数的间距的通用函数，以便可以针对两个圆柱体之间的任何给定距离获得它们。该模型能够捕获锁定范围和最大振幅。