MATEC Web of Conferences 24 , 0 6 0 0 2 (2015)
DOI: 10.1051/ m atec conf/ 201 5 2 4 0 6 0 0 2
C Owned by the authors, published by EDP Sciences, 2015
DYNAMIC TESTS ON A CONCRETE SLAB WITH A TUNED MASS
DAMPER
Jorge Eliécer Campuzano Carmona1, Suzana Moreira Avila2,Graciela N. Doz 3
1
UNB, University of Brasilia, Department of Civil Engineering, Brasília, Brazil.
UNB, University of Brasilia, Faculty of Gama FGA, Department of Civil Engineering, Brasília, Brazil.
3
UNB, University of Brasilia, Department of Civil Engineering, Brasília, Brazil.
2
Abstract. Nowadays, structures became more slender and flexible due to lighter materials with great resistance,
compared to traditional materials used in construction. This fact provides to structural systems with low natural
frequencies. High amplitude vibrations can be experienced, when the structures are subjected to people walking,
running, jumping, dancing, activities that are characterized by periodical low frequency forces. Various solutions can
be taken, such as techniques to stiffen all the structure, which can result a non-economical solution and not practical.
Other alternative that can be more economical and executable is to install tuned mass dampers (TMD) at the building
structure, that vibrate out of phase with the main system, transferring the mechanical energy to the additional mass. In
this work, excessive vibrations in concrete slabs are studied through testing a dynamic platform very flexible where it
is installed a TMD. The tests simulate human activities such as walking, jumping or dancing. Vibrations amplitudes of
the platform are compared with and without TMD installation, finding a good reduction on these amplitudes with this
structural control device. The TMD designed has a dry friction mechanism to reduce the response of the additional
mass, controlling excessive vibration caused by human activities in building floors. Keywords: Tuned Mass Damper,
Damping, Modal Analysis, Frequency-Domain Analysis, Time-Domain Analysis, MAC
1 Introduction.
Nowadays, new structures are more and more slender and
flexible with longer spans, presenting low natural
vibration frequencies.
More flexible structures implicate on higher vibration
amplitudes that are transmitted to people using these
rooms affecting human activities such as feet and hands
movements
To solve this problem on civil structures such as offices,
commercial areas, gyms, dancing clubs, laboratories,
theaters and footbridges, structural control devices such
as tuned mass dampers (TMD) can be installed.
TMD are designed to have a fundamental frequency
value near one of the main structure frequencies, in a way
that a portion of the energy is transferred to the TMD
reducing excessive vibrations. This type of damper has a
good performance, reducing vertical and horizontal
vibrations in real structures such as Millennium Bridge,
London [1], Marina Bay Sands Hotel, Singapore [2], a
Abandoibarra Footbridge, Spain [2], Rio Niterói Bridge,
Rio de Janeiro, Brazil [3].
of values of the characteristics frequencies values of
walking, jumping and dancing: between 1,5 Hz and 5,5
Hz for first and second harmonic [6]. For obtaining these
dynamic characteristics numerical and experimental
studies were performed. On Table 1 it is presented the
numeric modal analysis results with the three first natural
frequencies of the platform.
Table 1. Numerical natural frequencies
Numerical Study
Frequency 1
3.36 Hz
Frequency 2
15.67 Hz
Frequency 3
23.64 Hz
The numerical TMD optimal parameters were: vibrating
mass 120 kg, damping coefficient 360 Ns/m and stiffness
51000 N/m. With these optimal values it was constructed
the TMD presented on Figure 1.
2 TMD and main structure description.
TMD was designed with ANSYS software [4], mass,
damping and stiffness parameters were found out. Those
parameters were set, tuning the damper to the main
structure: a dynamic test platform with 6,1 m length and
4,9 m width and 0,1 m thickness [5] that presents a
fundamental frequency of 3,32 Hz, i.e. within the range
Figure 1. TMD attached to the dynamic platform with two
vibrating mass sets.
georcam2003@hotmail.com avilas@unb.br graciela@unb.br
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152406002
MATEC Web of Conferences
3 Experimental test descriptions
Table 2. Experimental frequencies of the four tests.
To determine the first experimental natural frequencies of
the platform, 4 tests were performed.
The instrumentation consisted of two piezoelectric
accelerometers (PCB Piezotronics), one fixed in the
center of the slab (node 41 - tests 1 and 4) or on the slab
corner (node 20 - tests 2 and 3) and other mobile that
changed position through the structure as shown in
Figure 2 and Figure 3.
The accelerometers were connected to a signal processor
ADS2000 that is connecter to a computer. The tests were
performed exciting the slab on the platform center with
impact produced by the drop heel for a second and letting
the structure vibrate for 14 seconds. Acceleration records
were processed by ARTeMIS software [7] and the first
four modal shapes with corresponding frequencies were
obtained (Table 2).
Freq #
F1
F2
F3
F4
F5
Test 1
3.42Hz
15.53Hz
23.24 Hz
85.25 Hz
-----
Test 2
3.32 Hz
15.14 Hz
22.95 Hz
31.35 Hz
48.63 Hz
Test 3
3.32 Hz
15.23 Hz
----51.76 Hz
-----
Test 4
3.32 Hz
15.33 Hz
23.05 Hz
91.99 Hz
-----
Figure 4 shows time history acceleration and Figure 5
this record Fourier transform indicating the first slab
frequencies.
Time-Domain Analysis
3.5
Acceleration [m/s²]
2.5
1.5
0.5
-0.5
-1.5
-2.5
-3.5
0
5
15
10
Time [s]
Figure 4. Time-history acceleration, Test 4.
Frequency-Domain Analysis
4.5
3.32
4.0
3.5
81 Nodes
3.0
2.5
Figure 2. 81 node mesh to obtain acceleration records.
2.0
1.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
42
43
44
45
37
38
39
40
41
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
1.0
23.05
0.5
15.33
0.0
0
5
15
20
Frequency [Hz]
25
30
Figure 5. Frequency-Domain analysis, Test 4.
4.9 m
Table 3 present comparative results between numerical
and experimental analysis for the three first natural
frequencies of the structure.
Table 3. Comparative results between numerical and
experimental analysis for the three first natural frequencies of
the structure.
6.1 m
Figure 3. Node numeration of the experimental mesh.
10
Frequency 1
Frequency 2
Frequency 3
06002-p.2
Numerical
3.36 Hz
15.67 Hz
23.64 Hz
Experimental
3.32 Hz
15.33 Hz
23.05 Hz
% error
1.19 %
2.17 %
2.50 %
EVACES'15
From Figure 6 to Figure 8 it is shown the three first mode
shapes obtained through numerical simulation and
experimental procedures, respectively.
Figure 8. Third modal shape numerical ANSYS[ 4] and
experimental ARTeMIS[7].
Figure 6. First modal shape numerical ANSYS[4] and
experimental ARTeMIS[7].
The three first experimental modal shapes obtained using
ARTeMIS [7] are consistent with those obtained
numerically with ANSYS [4].
From the experimental and numerical results it was
performed a Modal Assurance Criterion MAC study and
the results are show on Figure 9 to Figure 12. These
values are close to 1 for the first modal shape, this means
that both the numerical values as the experimental values
are mutually consistent. On the main diagonal of MAC
matrix it is found out the combination of the three first
modal shapes numerical and experimental, being more
satisfactory the results for the first and second modes.
MAC Test 1
0.987
0.998
1.0
0.864
0.8
0.6
0.4
4 mod exp
3 mod exp
2 mod exp
1 mod exp
0.2
0.0
1 mod
Num
2 mod
Num
3 mod
Num
4 mod
Num
Figure 9. Modal assurance Criterion Test 1.
Figure 7. Second modal shape numerical ANSYS[ 4] and
experimental ARTeMIS[7].
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MATEC Web of Conferences
Table 4 present TMD spring stiffness. The 10 springs
were divided in two sets as it can be noticed in Figure 1.
On Table 5 it is presented the weights obtained
experimentally of each piece that constitute the vibrating
mass of the TMD.
MAC Test 2
1.0
0.974
0.998
0.887
0.8
0.6
Table 4. TMD stiffness.
0.4
0.2
0.0
1 mod 2 mod
Num Num 3 mod 4 mod
Num Num 5 mod
Num
5 mod exp
4 mod exp
3 mod exp
2 mod exp
1 mod exp
Module 1
Module 2
Spring 1
5550.4
Spring 6
5351.5
Spring 2
5130.2
Spring 7
5296.6
Spring 3
5254.0
Spring 8
5314.9
Spring 4
4957.6
Spring 9
5249.1
Spring 5
4978.7
Spring 10
5428.4
Σ
K= 52511.4 N/m
Figure 10. Modal assurance Criterion Test 2.
MAC Test 3
0.956
0.998
Table 5. TMD masses.
1.0
0.8
Module 1
Plate1+12 Rings
0.6
0.8
Plate 2
Plate 3
Plate 4
Plate 5
Plate 6
Plate 7
Plate 8
Plate 9
Plate 10
Plate 11
Plate 12
Screw 1
Screw 2+Piece
0.6
Piece+ screw nut
0.4
3 mod exp
0.2
2 mod exp
0.0
1 mod Num
1 mod exp
2 mod Num
3 mod Num
Figure 11. Modal assurance Criterion Test 3.
MAC Test 4
0.998
0.979
1.0
0.890
Module 2
5022.9
4880
4850.4
4792
4813.8
4784.8
4838.4
4878.7
4806.5
4878.7
4947.1
4726.5
203.9
801.6
1036.2
Σ
0.4
4 mod exp
3 mod exp
2 mod exp
1 mod exp
0.2
0.0
1 mod
Num
2 mod
Num
3 mod
Num
Plate14+12 Rings
Plate 15
Plate 16
Plate 17
Plate 18
Plate 19
Plate 20
Plate 21
Plate 22
Plate 23
Plate 24
Plate 25
Screw 1
Screw 2+Piece
Piece+ screw nut
4963.3
4820
4792.5
4795.7
4853.7
4738.8
4734.4
4882.1
4792.9
4860.6
4851.3
4826.5
207
786.7
1040.8
M = 120207.8 g
From the above experimental parameters of mass and
stiffness it is possible to calculate the TMD frequency:
4 mod
Num
Figure 12. Modal assurance Criterion Test 4.
f
3.1 Experimental tests with the TMD attached
As it can be observed on Figure 4 the platform present
high accelerations of about 3.0 m/s² that are out of the
recommended limits by international codes [6]. To reduce
acceleration a TMD was designed and installed at the
slab center coinciding with the point of the highest first
modal displacement. (Figure 1). The TMD vibrating mass
is composed of several steel plates with 12,5 mm
thickness, with several holes of 14 mm of diameter on its
surface. The system stiffness is obtained through steel
springs with coils of 2,5 mm of diameter and height of 65
mm. The damping system is obtained with two vertical
axes that generate dry friction with two small steel block.
1
2S
1
K
Ÿ
2S
M
52511.4 kg s 2
120.2078kg
3.33Hz
(1)
The experimental TMD natural frequency was obtained
installing accelerometer on the vibrating mass and
extracting a 20 s record. On Figure 13 on the frequency
domain response it is possible to verify the TMD
experimental frequency with a value of 3.516 Hz.
06002-p.4
EVACES'15
Thus records from different tests were compared to verify
TMD performance. For the different tests three
accelerometers were placed on the slab surface and a
fourth accelerometer on the TMD vibrating mass. The
accelerometers distribution can be seen on Figure 15.
35
3.516
30
3.516
25
3.516
20
15
10
5
0
0
1
2
3
4
5
6
Frequency [Hz]
7
8
9
10
Figure 16 presents an acceleration time history when the
structure is excited by an harmonic force of a person with
semi flexed knees on the edge of the slab during 10
seconds, considering the without TMD situation (red line)
and with the TMD attached (blue line). Figure 17 shows
the corresponding frequency response.
Figure 13. Frequency response of the TMD vibrating mass.
Having the above results of the TMD frequency 3,516 Hz
and the main structure fundamental frequency of 3,32 Hz
it was calculated the experimental frequency ratio β that
was about 1,059. The mass ratio was calculated using the
TMD vibrating mass 120.2 kg and the theoretical value of
the slab mass, approximately 7173.6 kg. With these mass
values, the mass ratio was of µ=1.676%.
247
195
108
201
106
490
Accelerometer 1 Accelerometer 2 Accelerometer 3
Concrete Slab
The accelerometer installed on the TMD vibrating mass
to find out the damper natural frequency is shown on a
Figure 14.
610
Acceleration [m/s²]
Figure 15. Accelerometer distribution (cm)
Accelerometer
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
Test with TMD
Test without TMD
0
Figure 14. TMD installed with accelerometer 353B33.
2
4
6
8
10
12
14
16
18
20
Time [s]
Figure 16. Acceleration time-history - with and without TMD –
semi flexed knees test.
3.2 Experimental tests of rhythmic activities.
32
With TMD tuned into a frequency near of the main
structures resonance frequency and attached to the
structure tests with rhythmic activities were performed to
verify TMD performance. The tests were basically repeat
several times a people or a group of people (2, 3, 4 and 5
people) walking synchronously or not for 20 seconds. It
was also performed tests with a person jumping
continuously at the center of the platform during 10
seconds and also groups of 3 and 5 individuals,
distributed all over the slab. Synchronized tests with
people with the knees semi flexed trying to simulate an
harmonic force also were performed. As well it was
simulated an impact force by a person jumping from a
chair and letting the slab vibrate. It is noteworthy that all
the tests were done the same way in a repetitive way,
with coupled TMD and without TMD.
3.22; 30.48
28
Test with TMD
Test without TMD
24
20
16
12
8
3.22; 2.17
4
3.71; 2.76
0
0
1
2
3
4
5
6
Frequency [Hz]
7
8
9
10
Figure 17. Frequency response - with and without TMD - semi
flexed knees test.
06002-p.5
MATEC Web of Conferences
On the time domain analysis without TMD it can be
observed that the maximum positive acceleration was of
11,13 m/s² and the maximum negative acceleration was
of -10,39 m/s², however for records with the TMD
attached the maximum positive acceleration was of 2,70
m/s² and the maximum negative acceleration was of -3,14
m/s². For positive accelerations it represents a reduction
of 75,74% and for negative accelerations a reduction of
69,78 % installing the TMD on the platform. Verifying
frequency response analysis it can be noticed that a
reduction of about 11 times on vibration amplitude, about
a 90,94 % reduction and the appearance of a new
structure natural frequency of 3,71 Hz.
that on Figure 18 after getting off the excitation force the
TMD reduces accelerations a very low levels near to zero
on a time interval of 2 seconds. In the case of the
uncontrolled structures it takes about more than 9 seconds
to the structure stop vibration. For continuous jumping
tests of one person on the slab center Figure 19 also
presents an amplitude vibration reduction of even 3,18
times, modifying the vibration frequency form 3,42 Hz to
3,61 Hz. Other continuous jumping tests with groups of 3
and 5 people were performed as shown in Figure 20.
On the test simulating an harmonic force it can be said
that the TMD reduces quickly the accelerations in less
than 2 seconds after the appliance of the external load.
Tests with continuous jumping of a person during 10
seconds on the center of the platform, results on time and
frequency domains domain are presented on Figure 18
and Figure 19 respectively.
10
Test with TMD
Test without TMD
Acceleration [m/s²]
8
6
Figure 20. Continuous jumping tests with a 5 people group.
4
2
0
-2
-4
-6
-8
0
2
4
6
8
10
12
Time [s]
14
16
18
20
Tests with people walking all over the slab surface
randomly during 20 seconds with 2, 3, 4 and 5 people
group were also performed. On Figure 21 and Figure 22,
it is presented the time and frequency domain,
respectively, for a group of 4 people walking randomly.
Figure 23 show people walking randomly around the
dynamic platform.
Figure 18. Time-Domain analysis with and without TMD –
continuous jumping during 10 seconds
Acceleration [m/s²]
27
3.42; 25.71
24
Test with TMD
Test without TMD
21
4
18
15
12
2
1
0
-1
-2
-3
3.61; 8.08
3.22; 7.37
9
Test with TMD
Test without TMD
3
-4
6
3.13; 1.90
3
0
3.32; 1.80
0
0
1
2
3
4
5
6
Frequency [Hz]
7
8
9
10
2
4
6
8
10
12
Time [s]
14
16
18
20
Figure 21. Time-Domain analysis with and without TMD –
walking test.
Figure 19. Frequency-Domain analysis with and without TMD.
Continuous jumping during 10 seconds
On these tests it can also be observed a reduction on
acceleration amplitudes records when the TMD is
attached to the platform. On Figure 18 acceleration
records in blue shows to be more regular due to the TMD
action. Comparing Figure 16 with Figure 18 it can be said
that the damper has a better performance to loadings
more similar to harmonic force than those for nonuniform excitation forces like continuous jumping
impacts In the same way of Figure 16 it can be observed
06002-p.6
EVACES'15
4.5
3.42; 4.40
4
43.51%
Test with TMD
Test without TMD
Accelerometer 2
3.5
2.87 0.01%
2.47 0.07%
1.15%
4.22%
7.42%
2.07 0.22%
1.67
1.27
0.87
0.47
10
Acceleration [m/s²]
Figure 24. Acceleration relative frequency with TMD –
continuous jumping test 10 seconds
11.93 0.02%
10.34 0.24%
1.37%
4.50%
0.54%
8.76
7.18
5.60
4.02
-0.73
7.26%
Accelerometer 2
9.73%
10.01%
-2.31
4.91%
7.85%
-3.89
1.43%
-7.06
-5.48
0.51%
-8.64
-10.22 0.22%
29.07%
22.34%
Figure 22. Frequency-Domain analysis with and without TMD
- Walking test.
2.43
9
0.07
8
-0.33
7
0.85
4
5
6
Frequency [Hz]
-0.74
3
2.01%
2
-1.14
1
0.57%
0
-1.54
0
-1.94
-2.74 0.06%
1
0.5
-2.34 0.11%
3.13; 1.53
1.5
5.54%
2
11.04%
16.65%
3.32; 2.69
3.13; 2.62
7.41%
3
2.5
Acceleration [m/s²]
Figure 25. Acceleration relative frequency without TMD –
continuous jumping test 10 seconds
Figure 23. Test with people walking randomly.
From Figure 21 it can be observed that the damper
performance is not so good like on the previous tests,
however the TMD still reduces vibration amplitudes. On
Figure 22 it can also be observed a response when using
the TMD. Analyzing Figure 16 to Figure 22 it can be
concluded that the damper presents a better performance
on the harmonic loading case.
It is also presented on Figure 26 and Figure 27 the
histogram of acceleration frequencies relative to
accelerations obtained on tests of harmonic force
simulation, with and without control, respectively. It can
be observed that the control system reduces the response
effectively, around 75 % of the acceleration records are
approximate to 0,22 m/s².
75.06%
3.3 Statistical analysis of experimental tests
considering rhythmic activities.
11.74 0.03%
10.24 0.04%
8.75 0.06%
7.25 0.27%
5.76 0.37%
4.26 0.64%
9.49%
3.43%
2.77
1.27
-0.22
7.01%
-1.72
2.45%
-3.21
-4.71 0.57%
-6.20 0.26%
-7.70 0.19%
-9.19 0.12%
Results obtained from the above experimental program
were analyzed through a statistical treatment. For
repeating tests of continuous jumping with the TMD
attached it was built an histogram of acceleration
frequencies. Results for acceleration mean are presented
on Figure 24. On Figure 25 it is presented results of the
same tests without control. Comparing the graphs it can
be observed that the histogram fifteenth class with control
shows a great acceleration reduction from 11,93 m/s²
without control to 2.87 m/s² with control, presenting
almost the same percentage of acceleration mean of 0,02
%. It can also be observed from the histogram with
control that maximum percentage of acceleration is
around of the mean value of 0,07 m/s², what represents a
good reduction of acceleration records comparing the
same test without control.
Accelerometer 2
Acceleration [m/s²]
Figure 26. Acceleration relative frequency with TMD –
harmonic force.
06002-p.7
MATEC Web of Conferences
4 Conclusions.
26.12%
0.80%
10.40
4.34%
4.65%
7.53
8.97
4.37%
6.10
4.69%
4.67
5.23%
3.23
7.96%
1.80
0.36
-1.07
6.43%
-2.51
5.07%
5.18%
-3.94
-5.38
5.00%
-6.81
5.33%
-8.25
-9.68
1.35%
13.46%
Accelerometer 2
Acceleration [m/s²]
Figure 27. Acceleration relative frequency without TMD –
harmonic force.
On Figure 28 and Figure 29 it is presented the histogram
of acceleration frequencies considering people walking
randomly. There is a light reduction of the mean
accelerations with control (blue histogram) comparing
with mean acceleration without control (red histogram).
21.20%
20.42%
2.37 0.07%
2.04 0.24%
1.88%
0.77%
1.71
1.37
0.71
0.37
0.04
-0.29
-0.62
1.04
4.84%
6.77%
2.14%
-0.96
0.85%
-1.62
-1.29
0.29%
-1.96
-2.29 0.08%
Accelerometer 2
9.83%
11.87%
18.75%
Acceleration [m/s²]
Figure 28. Acceleration relative frequency with TMD – people
walking
Accelerometer 2
It also presents good performance reducing vibration
caused by impact loads. It was observer that it worked
better when the excitation force is greater that the induced
force by people walking. The proposed TMD is
characterized by its low cost of fabrication and it is also
easy to build and maintain.
References
[1] GERB Schwingungsisolierungen GmbH & Co. KG.
Vibration Protection for Structures. Buildings .
Machinery and other Equipment with Tuned Mass
Dampers. (2001).
[2] Maurer Sönhe. Tuned Mass and Viscous Dampers.
Technical information and products. Structural Protection
Systems. 13 (2011).
[3] R.C. Battista, M. S. Pfeil. Control of Wind
oscillations of Rio-Niterói bridge, Brazil. Proceedings of
the Institution of Civil Engineers. ICE. Structures and
Buildings 163 p 87-96. April (2010).
[4] ANSYS. Swanson Analysis System. Version 14.5.
(2012).
[5] Campuzano. J.E., Doz. G. N., Avila. S.M. Study
Design and Construction of a Tuned Mass Damper
(TMD) For concrete building floors. Proceedings of the
9th International Conference on Structural Dynamics,
EURODYN. 1761-1768 (2014).
[6] Murray. T.M.. Allen. D.E.. Ungar. E.E. Floor
Vibrations Due to Human Activity. Steel Design Guide
Series. American Institute of Steel Construction. Second
printing. October (2003).
[7] ARTeMIS modal 4.0.
3.495 0.07%
2.23%
2.995 0.26%
2.495
1.996
3.97%
1.496
0.997
0.497
-0.003
-0.502
0.89%
9.60%
8.48%
-1.002
2.10%
4.90%
-1.502
-2.001
0.95%
-2.501
-3.000 0.18%
-3.500 0.05%
18.83%
19.19%
28.29%
A tuned mass damper was designed and then tested, it
showed to be an effective structural control device on
mitigating vibrations produced by harmonic forces on a
concrete slab.
Acceleration [m/s²]
Figure 29. Acceleration relative frequency without TMD –
people walking
06002-p.8