Investigation On Self-excited Vibration Of2-Dof Cylinder Under Multi Boundary Conditions

Though much attention has been paid to and a series of in-depth investigation has been launched for vortex induced vibration(VIV) of cylinder,there is no clear explanation about the effect of freedom on VIV response,and how parameters such as frequency ratio,mass damping ration together with Reynolds number influence the2-Dof VIV needs a comprehensive study. Meanwhile,relationship between cylinder vibration amplitude curves and main parameters still needs to becarefully determined. Academic Committee in2011ITTC supplies the benchmark only for single degree of freedom vortex-induced vibration,while there is a lack of authority criteria for2-Dof VIV and column groups. Experimental investigantion of2-Dof VIV is carried out in this paper under multi boundary conditions,and the influence of natural frequency,mass damping ratio and Reynolds number on VIV characteristics of cylinders with different scales is systematic studied based on the results of more than one thousand test cases,also the latest research results of VIV for elastic supported cylinder in the world.Effect of natural frequency and frequency ratio between In Line(IL)direction and Cross Flow(CF)direction on vibration amplitude, frequency, phase and also the trajectory was explored in this paper by adjusting the spring stiffness horizontally and vertically.Investigantion results imply that when keeping the CF natural frequency as a constant, increasing the stiffness of the IL direction will lead the CF peak amplitude to decrease and move towards to higher reduced velocity and "Twin Peaks" response is observed under high frequency ratio. As a special case of2Dof VIV with an infinite IL stiffness, single degree of freedom vortex-induced vibration demonstrates a relatively small amplitude, but the peak will occur at a relatively low amplitude of reduced velocity.Frequency ration between IL and CF direction shows significant effect on determining the relative phase angle, thereby affecting the trajectory of the cylinder vibration.The increase of frequency ratio leads the gradual increase of phase angle,making the lobes of the "eight" trajectory point towards the upstream flow direction.and the transition frequency ratio at which the lobes point towards from downsream to upstream decreases with the increase of CF natural frequency.Should the IL natural frequency was kept as an constant,the decrease of CF stiffness would make the peak amplitude appear at a relatively higher reduced velocity, this law is especially seen in test cases with low IL natural frequency.However,there appears no uniform increase or decrease of the vibration amplitude when changing the CF stiffness.Meanwhile.the change of CF stiffness shows impact on the relative phase angle and viration trajectory, especially for lower IL natural frequency cases. The transition frequency ratio increases with the increase of IL natural frequency.Three high-order harmonic component appears in PSD of CF vibration acceleration, which is not the case in CF motion,indicating the generation of’2T" vortex pattern.Different form other studies,in this experimental investigation, fundamental CF frequency and four-order CF frequency were found in PSD of both the IL vibration acceleration and IL motion.This frequency component leads new vibration trajectories to appear:"D","egg","raindrop","deformity8"and" TwinView8"shape,which are different from traditional concept of8"shape and" crescent "shape.In this paper."non-linear spring pendulum in resonance" model is presented to describe the2-Dof VIV,considering the finding of the fundamental CF frequency and four-order CF frequency in IL direction.Effects of mass damping ratio and Reynolds number on vibration response was investigated in this paper.Results show that for cylinders with the same natural frequency,there in no significant impact on the vibration amplitude w;hen changing the mass damping ratio,and the peak amplitude corresponds to the same reduced velocity,while for low mass damping ratio case, high amplitude corresponds to a slightly broader range of reduced velocity.Should the system stiffness was kept the same for different cylinders.high vibration amplitude will appear at higher reduced velocity when decrese the mass damping ratio,and the range of resonance was expanded compared to high mass damping ratio cases.Significant impact was seen of Reynolds number on response branch and peak amplitude.which shows higher rate of influence than mass damping ratio.For high Reynolds number, typical response with three branches was found,namely initial,upper and lower branches,also the higher peak amplitude and broader rang of upper branch.While the decrease of Reynolds number would result in lower peak amplitude and the occurance of "lock in" at a lower reduced velocity.Besides,the upper branch disappears gradually and vibration amplitude shows only the initial branch and lower branch.