Vibration suppression of a 90-m-tall steel

The Eighth East Asia-Pacific Conference on Structural Engineering and Construction
5-7 December 2001, Nanyang Technological University, Singapore
VIBRATION SUPPRESSION OF A 90-M-TALL STEEL STACK BY USING
A HIGH-DAMPING TUNED MASS DAMPER
Natthapong Areemit 1 , Pennung Warnitchai 2
ABSTRACT: This paper presents an application of a pendulum tuned mass damper to suppress wind-induced
oscillation of a 90-m-tall steel stack in Rayong, Thailand. During the design phase, an analysis of wind-induced
response of the stack was carried out, and it was found that unacceptably large sway motions of the stack could
be developed even at low wind speeds due to vortex resonance. It was also found that the sway motions could be
effectively suppressed by introducing sufficiently high additional damping to the stack. A pendulum Tuned Mass
Damper (TMD) was then chosen as a vibration control device to be installed at the top of the stack. It consists of
a 3600-kg steel ring, three suspended wire ropes, and three viscous dampers. The damping ratio of TMD was
intentionally set to a value much higher than the optimal one; this was to keep the relative motion between TMD
and the stack within an acceptable limit and to make the performance of TMD less sensitive to the error in
frequency tuning. Performance tests of the pendulum TMD were conducted before and after the installation to
the stack. The tests before the installation indicated that the natural frequency of TMD varied significantly with
the vibration level. This was caused by the change in effective pendulum arm length, and the mechanism was
carefully investigated in details. The tests also revealed a viscoelastic effect of the dampers; the dampers not
only added damping to the pendulum system but also shortened the natural period of the system. Despite the
variation of natural frequency and the viscoelastic effect, the tests after the installation showed clearly that
sufficiently high damping was added into the stack system.
KEYWORDS: Tuned Mass Damper, Steel Stack, Vortex resonance, High Damping
1. INTRODUCTION
This is a story of a 90-m-tall steel stack located inside an industrial plant in Rayong province,
Thailand. The stack is an unlined, welded, free-standing structure with circular cross section. As
shown in Figure 1 the diameter of the stack varies from 2.20 m at the top to 5.50 m at the base, and the
shell thickness varies from 12 mm to 22 mm. The natural frequencies of the first and second sway
modes are estimated by an FEM analysis to be 0.84 Hz and 3.52 Hz, respectively. The corresponding
mode shapes are illustrated in Figure 1. The modal mass of the first mode is 29,000 kg (the mode
shape is normalized such that its value at the top is unity), while the total mass is 196,000 kg.
During the design phase, several analyses of wind-induced responses were carried out in order to
predict the stack’s motions in both along-wind and across-wind directions. The well-known
Davenport’s frequency-domain analysis procedure was employed for the along-wind case, while the
Vickery-Basu’s procedure was adopted for the across-wind case [1]. In these procedures, wind
excitation is treated as random lateral loading distributed nonuniformly over the entire height of the
stack. The obtained results indicate that the across-wind response is more critical than the along-wind
response due to an occurrence of vortex resonance. That is, the stack is likely to oscillate strongly in a
plane perpendicular to the mean wind direction during when the hourly mean wind speed at the
gradient height lies within a critical range of 15 to 25 m/s. The oscillation is caused by the vortex
resonance in the first sway mode; the contributions from other higher modes are found to be relatively
small. The oscillation amplitudes might even exceed 0.40 m in such a low wind speed range, and this
1 Khon Kaen University, Thailand, Lecturer
2 Asian Institute of Technology, Thailand, Associate Professor
Paper No.: 1316

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

stack can be expected, and the maximum relative movement is limited to 0.10 m as required. An
additional benefit from this adjustment is the improved robustness of TMD; the performance of this
high-damping TMD is less sensitive to the error in frequency tuning compared to the case of the initial
design. This robustness is one of the key factors for the success in the application of this TMD—this
point will be discussed in the following sections.
(a) (b)
(c) (d)
Figure 2 Pendulum TMD and its components: (a) steel ring, (b) viscous damper, (c) suspended
wire rope, (d) drawings showing the assembly
3. PERFORMANCE TESTS
A
Stack
Pendulum
mass
Stack
Suspended cable
Pendulum mass
Damper
Section A - A
To ensure damper effectiveness, performance tests were carried out in six stages. The objective of
tests in the first three stages was to separately identify the dynamic properties of the pendulum TMD
and the stack. The fourth-stage test was made to check the dynamic properties of the combined stack-
TMD system. Tests in the last two stages were carried out to examine the control effectiveness of
TMD under normal service conditions.
In the first stage, the pendulum system without viscous dampers was installed on the top segment of
the stack in the fabrication yard as shown in Figure 3. The segment was firmly locked to the floor, so
that it acted like a motionless supporting frame for the pendulum. Two uniaxial acceleration sensors
were placed on the ring to measure its motions in two horizontal orthogonal directions. The
acceleration signals were recorded by a portable data acquisition unit. By this way, the natural
frequency and damping ratio of the pendulum could be easily identified from its free vibration records.
The obtained free vibration records indicate that vibration frequency is strongly dependent on
vibration amplitude (Figure 4 a and b). This amplitude dependent characteristic could not be explained
by the geometric nonlinearity of the pendulum, which causes almost negligibly small variation in
vibration frequency within the measured amplitude range. It was observed, however, that when the
vibration amplitude was small, the two ends of suspended ropes were practically clamped to the

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).

Acceleration, g
0.004
0.002
0.000
-0.002
-0.004
0 20 40 60 80 100
Time, seconds
Figure 7 Random vibration of the stack under natural wind
Normalized autocorrelation function
1.00
0.10
0.01
With TMD
W ith unlocked TMD
ξ = 0.5 %
0 10 20 30
nth Cycle
Figure 8 Autocorrelation envelope of the stack with locked TMD and with unlocked TMD
4. CONCLUSIONS
An application of TMD to suppress wind-induced vibration of the steel stack has been successfully
carried out. The well-known optimal design theory for TMD could not be applied in this case. The
damping ratio of TMD was instead set to a much higher level than the optimal value in order to keep
the relative motion between TMD and the stack within an acceptable limit. This also made TMD more
robust: the control effectiveness of this high-damping TMD was much less sensitive to the error in
frequency tuning compared to the case of optimally designed TMD. The robustness was a crucial
factor for the successful application of TMD because performance tests of TMD before the final
installation showed that TMD’s frequency was strongly amplitude dependent. In addition, tests also
revealed a viscoelastic effect of the viscous dampers; the dampers not only added damping to the
pendulum system but also shortened its natural period. Despite the variation of natural frequency and
the viscoelastic effect, performance tests after the installation of TMD showed clearly that sufficiently
high damping has been successfully introduced into the stack.
5. REFERENCES
[1] Simiu, E., Scanlan, R.H., 1985, “Wind Effects of Structures: An Introduction to Wind
Engineering”, 2 nd ed., NewYork, John Wile & Sons.
[2] Fujino, Y., Abe, M., 1993, “Design Formulas for Tuned Mass Dampers based on a Perturbation
Technique”, Earthquake Engineering and Strutural Dynamics, vol. 22, pp. 833-854.
4.0 %
3.0 %
1.0 %
2.0 %