Vibration suppression of a 90-m-tall steel

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).