Vibration suppression of a 90-m-tall steel

could lead to an extremely high rate of fatigue damage accumulation and, consequently, an extremely
short service life of the stack.
The across-wind response analysis results show that the vortex-induced oscillation can be effectively
suppressed by adding an additional damping to the stack. The damping of unlined, welded steel stacks
reported in the literature normally lies within a range of 0.2 to 1.0 % of the critical damping, and this
could lead to excessively high oscillation amplitudes as mentioned earlier. However, if the damping is
raised to 2, 3, 4 and 5%, the maximum oscillation amplitude will be reduced to, approximately, 0.14,
0.11, 0.09 and 0.08 m, respectively. It was considered that the damping of 2 % would be sufficient to
ensure the safety and serviceability of the stack. This could be achieved by installing a properly
designed Tuned Mass Damper (TMD) at the top of the stack.
90.0 m
10.0 m
20.0 m
30.0 m
30.0 m
2.20 m
3.20 m
4.10 m
5.20 m
(a) (b) (c)
Figure 1 (a) A 90-m-tall steel stack in Rayong, (b) its basic dimensions, and (c)the first and
second sway vibration mode shapes
2. DESIGN OF PENDULUM TUNED MASS DAMPER
1 st Mode 2 nd Mode
A simple pendulum-type TMD was chosen as a device to introduce the required additional damping to
the stack. It consists of a steel ring, three suspended wire ropes, and three viscous dampers as shown in
Figure 2. The design of this TMD was aiming at an additional damping of about 4 to 5 % of the
critical value. In the initial design, the well-known optimal design formulas for the case where the
main structure is subjected to stationary random loading were adopted [2]. The ring mass of 1500 kg
was found to be sufficient, and the corresponding optimal damping ratio of TMD was estimated to be
around 11 to 12 %. The optimal frequency tuning was achieved by setting the length of pendulum arm
to 0.38 m. With this optimal design, an additional damping in excess of 5 % could be expected.
However, the maximum relative movement between the ring and the stack was estimated to be as high
as 0.32 m. Such a large relative movement could lead to several problems in the design of viscous
dampers and could shorten the service life of suspended ropes. It was therefore considered that the
maximum relative movement must be limited to 0.10 m.
To satify this constraint, the initial design was adjusted by raising the TMD damping ratio to a level
much higher than the optimal level and, at the same time, raising the ring mass to compensate the
reduction in damper effectiveness. Note that the cost of TMD is not so sensitive to this adjustment
because the additional material cost of the steel ring is relatively low and the cost of viscous dampers
remain practically unchange for increasing levels of design damping coefficient. After a few rounds
of design adjustment, the final design was obtained: the ring mass was set to 3600 kg, and the TMD
damping ratio was set to 40 %. With this final design, an additional damping of about 5 to 6 % to the