Abstract:Based on the four-step semi-implicit characteristic line splitting operator finite element method, the vortex-induced vibration problem of two-degree-of-freedom tandem arrangement of double cylinders is numerically simulated, and the spacing ratio, shear ratio, natural frequency ratio and reduced velocity are analyzed. The influence of four parameters on the dynamic response of cylindrical structure.The study found:natural frequency ratio and shear ratio have a greater impact on the vibration amplitude of upstream cylinder. However, the impact of the natural frequency ratio and shear ratio on the downstream cylinder is small.The upstream cylinder reaches the maximum reduction speed in the two degrees of freedom direction is different, but the downstream cylinder is basically synchronized. The resonance area of the upstream cylinder is significantly wider than that of the downstream cylinder. Meanwhile, the time of upstream cylinder enter and exit the resonance area is earlier than that of the downstream cylinder. On the other hand, the two cylinders mainly complete the phase transition in the in-lock region. With the increase of the frequency ratio, the rate of the energy transfer from the fluid to the cylinder slow down, resulting in the slower rate of the cylinder complete the transition of in-phase to anti-phase. In the shear flow case, the phase difference between lift and displacement will appear “platform period” at the space ratio is more than 3.5. When the spacing ratio further increases beyond the critical value, with the increase of the reduced velocity, the more clutter frequency appears in the fluid force power spectral density curve, which leads to the phenomenon of energy “feedback”. Finally, in the uniform flow case, the main frequency value in the lift-drag power spectral density curve is twice the relationship, but as the shear rate increases, the fluid force power spectral density curve will basically coincide.