Abstract Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements are numerically investigated in a uniform flow at a low Reynolds number of 100. The oscillation system is restricted to the cross-flow direction, giving rise to a coupled two-degree-of-freedom response. Attention is placed on the two cylinders with a center-to-center gap ratio of 4 and a mass ratio of 10. The flow dynamics are described by the two-dimensional incompressible Navier–Stokes equations and resolved by the Characteristic-Based-Split finite element method. The stiffness of the first spring that connects the lower cylinder to the wall is chosen such that the vortex-induced vibration of the associated single cylinder with the same stiffness undergoes a pre-synchronization (state A), synchronization (state B) and post-synchronization (state C), respectively. In each state, the stiffness of the second spring connecting the lower and upper cylinders is varied to cover both synchronization and de-synchronization regimes. Numerical results show that the mechanically coupled system locks on the first-mode natural frequency in state A, while on the second-mode natural frequency in states B and C. In such a lock-in regime, the amplitude ratios of the two oscillating and coupled cylinders collapse well onto the corresponding first or second free-vibration mode. The overall coupling mechanism is further explained in terms of the hydrodynamic coefficients, frequency characteristics, wake patterns and effective added mass, quantifying the associated fluid-structure interactions against those governing a single-degree-of-freedom, single-cylinder system.

中文翻译：

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并排布置的两个具有非对称刚度的机械耦合圆柱体的涡激振动

摘要 在低雷诺数 100 的均匀流动中，数值研究了两个并排排列的非对称刚度机械耦合圆柱的涡激振动。耦合的二自由度响应。注意力集中在中心间隙比为 4 和质量比为 10 的两个圆柱上。 流动动力学由二维不可压缩 Navier-Stokes 方程描述，并由基于特征的分裂有限元求解元素方法。选择将下圆柱体连接到壁的第一个弹簧的刚度，使得具有相同刚度的相关单个圆柱体的涡激振动经历预同步（状态 A），分别是同步（状态 B）和同步后（状态 C）。在每种状态下，连接下气缸和上气缸的第二弹簧的刚度是变化的，以涵盖同步和去同步状态。数值结果表明，机械耦合系统在状态 A 锁定在第一模态固有频率，而在状态 B 和 C 锁定在第二模态固有频率。在这种锁定状态下，两个振荡和耦合的气缸很好地坍塌到相应的第一或第二自由振动模式。整体耦合机制在流体动力学系数、频率特性、尾流模式和有效附加质量方面得到进一步解释，量化了相关的流固耦合与控制单自由度的相互作用，