Vibration suppression of a 90-m-tall steel

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support pins due to the friction between them (Figure 5b). But when the vibration amplitude was large, slips occurred at the contact points, and the rope ends rotated almost freely around the pins (Figure 5c). By this mechanism, the effective pendulum arm length changed significantly during the decay of free vibration, and so did the vibration frequency. The control effectiveness of TMD could be greatly affected by this frequency change if the damping ratio of TMD were set to the optimal level as in the initial design. Fortunately, in this case the damping ratio was set to such a high level that the effectiveness of TMD was rather insensitive to this frequency change. Acceleration, g 0.50 0.25 0.00 -0.25 Figure 3 TMD installed on the top stack segment in the fabrication yard -0.50 0.50 0 10 20 30 0.01 0.10 1.00 Time, seconds Acceleration amp litude, g (a) (b) Figure 4 (a) Free vibration record of the pendulum system with no attached viscous dampers, and (b) computed vibration frequency from the record Frequency, Hz 0.80 0.70 0.60 a) b) c) Figure 5 Change in effective pendulum arm length
In the second stage, three viscous dampers were attached to the pendulum system, and free vibration test was carried out for this complete TMD configuration. It was found that, within the amplitude range of interest, the damping ratio was raised from 1–3 % to about 30 – 45 %, and the vibration frequency was also shifted from 0.61 – 0.67 Hz to about 0.78 – 0.88 Hz. The frequency shift could be explained by the fact that the viscous dampers generated not only viscous forces but also elastic forces; the dampers exhibited viscoelastic effect. In the third and fourth stage, free vibration tests were carried out after the construction of the stack was completed and TMD was installed on its top as designed. Acceleration sensors were placed on both stack and TMD. However, in the third stage the steel ring of TMD was locked such that it could not move relative to the stack; this was to check the dynamic properties of the stack. The sway motion of the stack was first induced by asking several people on the top platform to move their bodies back and forth in a synchronized manner at a frequency close to the estimated natural frequency. After a sufficiently high vibration amplitude had reached, these people were asked to stop moving their bodies, and the free vibration of the stack was measured and recorded. The vibration frequency and damping ratio of the stack were found to be 0.74 Hz and 0.7 %, respectively. After correcting for added masses of the ring and people, the natural frequency of the stack alone was estimated to be 0.80 Hz, which was close to the computed value from FEM analysis. In the fourth stage, TMD was unlocked, and the same free vibration test was repeated. Comparing to the previous stage, the decay of stack’s motion is much faster as shown in Figure 6. The effective damping of the stack with TMD computed from this response was about 3.6 – 4.5 %, which was less than the expected figure—5 %, but it was high enough to prevent fatigue damage and extend the service life to an acceptable level. Acceleration, g 0.20 0.10 0.00 -0.10 W ith unlocked TM D W ith locked TM D -0.20 0 5 10 Time, seconds 15 20 Figure 6 Free vibration responses of the stack with locked TMD and with unlocked TMD In the fifth and sixth stages, the responses of the stack with locked TMD and with unlocked TMD under natural wind excitation were measured in order to check the control performance in normal service conditions. The autocorrelation function of the random acceleration response of the stack in both stages looked like a cosine function of time with exponentially decreasing amplitude as expected. The decay rates showed that the effective damping of the stack increased from 0.5 % when TMD was locked to about 3.0% after TMD was unlocked. The effective damping was slightly lower than that obtained from free vibration tests. The difference was probably due to the fact that the level of measured random responses was much lower than the level of free vibration responses (compare Figure 6 with Figure 7).
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Vibration suppression of a 90-m-tall steel

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