Vortex-induced vibrations of a pivoted circular cylinder and their control using a tuned-mass damper
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Vortex-induced vibrations of a pivoted circular cylinder and control of these vibrations were investigated experimentally. A novel experimental setup was employed to reproduce orbiting response observed in some engineering applications. An adaptive pendulum tuned-mass damper (TMD) was integrated with the cylindrical structure in order to control the vortex-induced vibrations. All experiments were performed at a constant Reynolds number of 2100 for a range of reduced velocities from 3.4 to 11.3 and damping ratios from 0.004 to 0.018. For the experiments involving TMD, the TMD mass ratio was 0.087 and the TMD damping ratios investigated were 0 and 0.24. The results of the experiments performed without the TMD show that, in the synchronization region, the frequencies of transverse and streamwise vibrations lock onto the natural frequency of the structure. The cylinder is observed to trace elliptic trajectories. A mathematical model is introduced to investigate the mechanism responsible for the occurrence of the observed elliptic trajectories and figure-8 type trajectories reported in previous laboratory investigations. The results show that the occurrence of either elliptic trajectories or figure-8 type trajectories is governed primarily by structural coupling between vibrations in streamwise and transverse directions. Four types of elliptic trajectories were identified. The results show that the occurrence of the different types of elliptic trajectories is linked to phase angle between the streamwise and transverse vibrations of the structure, which depends on structural coupling. The results of the experiments performed to investigate effectiveness of the TMD in controlling vortex-induced vibrations show that tuning the TMD natural frequency to the natural frequency of the structure decreases significantly the amplitudes of transverse and streamwise vibrations of the structure. Specifically, the transverse amplitudes of vibrations are decreased by a factor of ten and streamwise amplitudes of vibrations are decreased by a factor of three. The results show that, depending on the value of the TMD damping ratio, the frequency of transverse vibrations is either characterized by the natural frequency or by two frequencies: one higher and the other lower than the natural frequency of the structure, referred to as fundamental frequencies. Independent of TMD damping and tuning frequency ratios, the frequency of streamwise vibrations matches that of the transverse vibrations in the synchronization region, and the cylinder traces elliptic trajectories. The phase angle between the streamwise and transverse vibrations is nearly constant when the pendulum is restrained. However, with the TMD engaged and tuned to the natural frequency, the phase angle fluctuates significantly with time. A mathematical model was utilized to gain insight into the frequency response of the structure. The results of the modeling show that the frequency of transverse vibrations is characterized by the fundamental frequency or frequencies of the structure and the frequency of streamwise vibrations is characterized by the fundamental frequency or frequencies as well as the first harmonic of the fundamental frequency or frequencies of the structure.