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Experimental study on control performance of tuned liquid column dampers considering different excitation directions
Mechanical Systems and Signal Processing 102 (2018) 59–71
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Experimental study on control performance of tuned liquid column dampers considering different excitation directions Ahmet Can Altunisßik ⇑, Ali Yetisßken, Volkan Kahya Karadeniz Technical University, Department of Civil Engineering, Trabzon, Turkey
a r t i c l e
i n f o
Article history: Received 26 October 2016 Received in revised form 17 April 2017 Accepted 15 September 2017
Keywords: Ambient vibration test Damping Dynamic response Ground motion Shaking table Tuned liquid column damper
a b s t r a c t This paper gives experimental tests’ results for the control performance of Tuned Liquid Column Dampers (TLCDs) installed on a prototype structure exposed to ground motions with different directions. The prototype structure designed in the laboratory consists of top and bottom plates with four columns. Finite element analyses and ambient vibration tests are first performed to extract the natural frequencies and mode shapes of the structure. Then, the damping ratio of the structure as well as the resonant frequency, head-loss coefficient, damping ratio, and water height-frequency diagram of the designed TLCD are obtained experimentally by the shaking table tests. To investigate the effect of TLCDs on the structural response, the prototype structure-TLCD coupled system is considered later, and its natural frequencies and related mode shapes are obtained numerically. The acceleration and displacement time-histories are obtained by the shaking table tests to evaluate its damping ratio. To consider different excitation directions, the measurements are repeated for the directions between 0° and 90° with 15° increment. It can be concluded from the study that TLCD causes to decrease the resonant frequency of the structure with increasing of the total mass. Damping ratio considerably increases with installing TLCD on the structure. This is more pronounced for the angles of 0°, 15°, 30° and 45°. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction In structural analyses of high-rise buildings, effect of lateral forces such as wind and earthquake should be evaluated in detail. These buildings may be exposed to the resonant condition under the lateral forces due to the low-frequency content. To avoid harmful effects of the resonant vibrations, the first solution to be considered is to increase the damping capacity of the structure. Seismic isolation, active, passive, semi-active control systems, and other supplemental damping systems are among the various alternatives to reduce the structural vibrations. In active control systems, external power is required to produce the forces to resist the dynamic forces acting on. In passive control systems, dynamic energy is absorbed in the system without any external power supply. Damping and stiffness of semi-active control systems can be controlled during the movement. Semi-active control systems need less energy than active ones. Among the passive control systems, Tuned Liquid Dampers (TLDs) is water confined in a container that uses the sloshing energy of water to reduce the dynamic response of the structure during excitation. TLDs are very effective for absorbing the low-frequency vibrations [1]. As a special case of TLD, Tuned Liquid Column Dampers (TLCDs) having U-shaped tube containing liquid that is usually water has been developed. TLCD can reduce the structural vibrations through the motion of liquid ⇑ Corresponding author at: Karadeniz Technical University, Department of Civil Engineering, 61080 Trabzon, Turkey. E-mail addresses: [email protected] (A.C. Altunisßik), [email protected] (A. Yetisßken), [email protected] (V. Kahya). https://doi.org/10.1016/j.ymssp.2017.09.021 0888-3270/Ó 2017 Elsevier Ltd. All rights reserved.
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residing in the container which counteracts the action of the external excitations [2]. The damping effect of TLCD is produced by the head loss of hydraulic pressure of the liquid due to the orifice installed inside of the container, and the viscous action in the boundary layers. Applications of TLCD on civil engineering structures were first proposed by Sakai and Takeda [3]. Balendra et al. [4] studied on the effectiveness of TLCD for vibration control of towers. Chang and Hsu [5] investigated the control performance of liquid column vibration absorbers for buildings. Gao et al. [6] used a numerical method to account for nonlinearity of the governing equation to determine the effectiveness of TLCD in controlling structural vibrations. Yalla and Kareem [7] performed an experimental study to examine the performance of a prototype semi-active TLCD. Wu et al. [8] proposed the guidelines for industrial practice related to the design of TLCD for damped single-degree-of-freedom structures under wind excitations. Wu et al. [9] summarized the optimal design parameters of TLCD using non-uniform cross-sections in horizontal motion. Chaiviriyawong et al. [10] simulated TLCD using an elliptical flow path estimation method. A modified version of TLCD is proposed by Al-Saif et al. [11] as a passive vibration control device at low-frequencies. Mousavi et al. [12] carried out a detailed investigation on the optimum geometry of tuned liquid column-gas damper for vibrations of an offshore jacket platform under seismic excitations. Sarkar et al. [13] proposed a passive hybrid type damper derived from a pendulum type tuned mass damper and a TLCD. Mensah and Dueñas-Osorio [14] developed a dynamic model of wind turbine to accommodate single/multiple TLCD to control the excessive vibrations. Bigdeli and Kim [15] compared three passive vibration control devices such as Tuned Mass Damper (TMD), TLD and TLCD experimentally. Behbarani et al. [16] showed the effect of TLCD with maneuverable flaps on the vibration control of structures. Ground motions due to earthquakes have three components with different intensities in lateral (longitudinal and transverse) and vertical directions. Almost all design codes suggested the simultaneous implementation of two lateral components such as in x- and y-directions of structures. However, the simultaneous effect of ground motion to whole structure in x- and y-directions is almost impossible. It can be more realistic approach to consider dynamic loads with different directions acting on the structure. This paper presents the experimental tests’ results for the control performance of Tuned Liquid Column Dampers (TLCDs) installed on a prototype structure exposed to ground motions with different directions. For this aim, a prototype structure and a TLCD are designed in the laboratory. They are exposed to the shaking table and ambient vibration tests for obtaining their dynamic characteristics. Finite element analyses are also performed for verification. Different excitation directions are considered by repeating the measurements within 0–90° excitation directions of 15° increment. 2. Analytical background Fig. 1 schematically shows a TLCD model. Equation of motion of liquid surface in TLCD was obtained by Gao et al. [6] with the aid of energy principles associated with the Lagrange’s equations as follows:
€ðtÞ þ y
1 f b €g ðtÞ _ _ þ x20 yðtÞ ¼ x tjyðtÞj yðtÞ 2 Le Le
ð1Þ
€g ðtÞ is the acceleration practiced to TLCD; y €ðtÞ, yðtÞ, _ where x y(t) are the acceleration, velocity and displacement of the liquid inside TLCD, respectively; Av, Ah are the vertical and horizontal cross-sections of TLCD, respectively; t is the cross-section ratio (Av/Ah); f is the damping ratio; x0 is the natural frequency of damper; Le is the total length of liquid in TLCD which can be calculated by
Fig. 1. Configuration of a TLCD system.
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Le ¼ 2h þ tb
61
ð2Þ
where h and b are the vertical and horizontal length of liquid columns. The natural frequency of TLCD can be determined by
sffiffiffiffiffiffi 2g x0 ¼ Le
ð3Þ
where g is the acceleration of gravity. 3. Experimental study 3.1. Prototype structure and its dynamic characteristics To evaluate TLCD effects on structural vibrations, a steel prototype structure consists of bottom and top plates and four columns is designed in laboratory. As a support/foundation element, the bottom plate with 300 300 10 mm dimensions is fixed to the shaking table using five bolts, one of them in the middle and others at the edge points. The top plate has 600 600 5 mm dimensions. Four columns, each of which 5 50 1000 mm dimensions, are welded to the top and bottom plates. Because our purpose is also to evaluate the control effectiveness of TLCD under the ground motion with different directions between 0° and 90° with 15° increment, the dimension of bottom plate is restricted, and chosen to be smaller than that of top plate (Fig. 2). Fig. 3 shows the geometric dimensions and laboratory construction models of the prototype structure. To extract natural frequencies and corresponding mode shapes, finite element (FE) model of the structure is constituted in ANSYS Workbench [17]. In FE model, the bottom plate of the structure is assumed to be fixed. The modal analyses are performed under a 244.5N dead load, and natural frequencies and mode shapes are obtained. Fig. 4 shows the FE model and the first mode shape of the structure. In Table 1, the periods, natural frequencies and mass participation ratios are given for the first three modes. For experimental validation, ambient vibration tests are performed on the structure using Operational Modal Analysis (OMA) method. In measurements, B&K3560 data acquisition system with 17 channels and B&K8340 type uni-axial accelerometer are used (Fig. 5). The signals are collected in the data acquisition system, and are transferred into PULSE [18] and OMA [19] software. The dynamic characteristics are extracted using Enhanced Frequency Domain Decomposition (EFDD) method in frequency domain and Stochastic Subspace Identification (SSI) method in time domain. Singular values of the spectral density matrices (SVDSM) of data set and the average of auto spectral densities (AASD) obtained from the EFDD method, as well as the stabilization diagram of estimated state of space model obtained from the SSI method are given Fig. 6. Comparison of numerically and experimentally obtained natural frequencies is given in Table 2. According to the FE analyses and experimental measurements, the resonant frequency of the structure is determined to be 2.61 Hz. To determine the damping ratio of the model structure, experimental studies are performed by using the shaking table with 500 500 mm dimensions, 500N weight and 1000N shaking capacity up to 1 g acceleration. Harmonic sinus waves are applied to the structure on the shaking table in resonant frequency with 1 mm and 2 mm amplitudes during 20 cycles. The time-histories of accelerations are measured from the harmonic vibration using two sensitive accelerometers located on the top and bottom plates of the structure. Butterworth-Bandpass technique is used in all data to filtrations of machine vibrations, and the frequencies between 0.1 Hz and 25 Hz are ignored. Logarithmic Decrement Method are used to calculate the damping ratios for different directions of motion between 0° and 90° with 15° increment. Five different measurements are taken for each case, and the averages of the measurements are used to determine the damping ratios. In addition, the maximum accelerations, velocities and displacements are calculated. Table 3 presents the maximum accelerations, velocities, and displacements, and the damping ratios of the structure for 1 mm and 2 mm amplitudes considering all cases. From this table, we can see that the structural responses decrease when the excitation direction changes from 0° to 90°. This is expected because stiffness of the columns becomes higher when increasing the direction from 0° to 90°. The damping ratios are slightly changed with changing the direction of motion except 90° direction. This is because the displacements for 90° angle are very small, and the calculation of damping ratio becomes difficult. 3.2. Tuned liquid column damper (TLCD) and its dynamic characteristics Before installing to the prototype structure, some structural properties of TLCD such as the resonant frequency, head-loss coefficient, damping ratio and water height-frequency diagram are determined experimentally by the shaking table test. Fig. 7 shows the geometrical properties of TLCD that is constructed by glass material glued each other with polysiloxane (silicone). Weight of the designed TLCD is 130.75N. The amplitude of excitation in harmonic tests is limited to allowable displacement of the structure and the water level in columns such that neither water surface falls below the horizontal portion of TLCD nor water pours out of the columns. TLCD is installed on the shaking table with the aid of four clamps. During the measurements, water heights are read by camera via rulers glued to the surface of glasses. Fig. 8 shows some view of TLCD on the shaking table before the measurements.
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Fig. 2. Dimensions of the bottom plate (units are in mm).
The experimental measurements are conducted using 16.4 cm initial water height (h) for 4 mm and 8 mm amplitudes, respectively. The maximum water heights are observed to be 19.8 cm and 21.4 cm at the frequency of 0.86 Hz for 4 mm and 8 mm amplitudes, respectively. According to this result, we can accept the resonant frequency of TLCD as 0.86 Hz. In Table 5, comparison of measured and calculated natural frequencies of TLCD is given. As seen, a difference of 7% is there between the natural frequencies measured by the shaking table tests and calculated by Eq. (3). This validates our experimental measurements. Fig. 9 presents Dh–Frequency diagram, which is plotted using data between 0.6 Hz and 1.1 Hz given in Table 4. As can be seen from Fig. 9 that maximum increases in water levels are 3.4 cm and 5.0 cm for 4 mm and 8 mm amplitudes, respectively. pffiffiffi The damping ratios are calculated by the half-power bandwidth method. Here, Y max = 2 point is marked on Y axis (see Fig. 9), and frequency ratios (x1 and x2) are then read on X axis. Damping ratios (n) for two different amplitudes (4 mm and 8 mm) are calculated and given in Table 6. The head-loss coefficients (d) is calculated by [4]
Fig. 3. Some views of the prototype structure.
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1st mode
Model structure
Fig. 4. Finite element model and the first mode shape obtained numerically.
Table 1 Dynamic characteristics of the model structure by the finite element method (FEM). Mode number
Period (s)
Frequency (Hz)
Mass participation ratio (%)
1 2 3
0.378 0.133 0.132
2.633 7.548 7.573
87.6 94.0 98.0
Fig. 5. Some views from the measurements and related equipment.
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a) Singular values of spectral density matrices of data set
b) Average of auto spectral densities of data set
c) Stabilization diagram of estimated state of space model Fig. 6. EFDD and SSI results.
Table 2 Comparison of the natural frequencies obtained by FEM and OMA. Mode number
FEM
1 2 3
2.633 7.548 7.573
pffiffiffiffi d ¼ 2L p
f
EFDD method
SSI method
Frequency (Hz)
Error (%)
Frequency (Hz)
Error (%)
2.596 6.916 8.440
1.40 9.14 10.0
2.613 6.901 8.390
0.76 9.37 9.74
Ymax
using the damping ratios and maximum water heights, and given in Table 6.
ð4Þ
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Table 3 Maximum accelerations, velocities and displacements, and damping ratios of the model structure measured for different excitation directions. Direction (deg)
1 mm amplitude Max. Accel. (g)
Max. Vel. (cm/ sn)
Max. Disp. (mm)
Damping Ratio (%)
Max. Accel. (g)
2 mm amplitude Max. Vel. (cm/ sn)
Max. Disp. (mm)
Damping Ratio (%)
0 15 30 45 60 75 90
1.299 1.281 0.919 0.620 0.278 0.123 0.092
60.740 68.690 54.630 36.540 16.360 5.710 1.419
39.190 47.300 37.490 25.830 1.112 0.560 0.420
0.699 0.499 0.512 0.713 0.405 0.671 3.267
2.292 2.317 1.910 1.358 0.620 0.207 0.111
114.960 121.880 105.310 70.440 34.160 9.730 2.612
76.720 78.560 66.390 42.460 20.330 0.553 0.600
0.739 0.695 0.699 0.450 0.775 0.939 2.577
Fig. 7. Geometrical properties of the designed TLCD (units in mm).
Fig. 8. Some view of TLCD system on shaking table before the measurements.
Fig. 9. Dh–frequency diagram for 4 mm and 8 mm amplitudes.
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Table 4 Change of the maximum water heights with frequencies in TLCD system. 4 mm amplitude
8 mm amplitude
Frequency (Hz)
Measured height (cm)
Dh (cm)
Frequency (Hz)
Measured height (cm)
Dh (cm)
0.610 0.650 0.700 0.735 0.746 0.758 0.769 0.780 0.790 0.806 0.820 0.830 0.850 0.860 0.870 0.880 0.890 0.900 0.940 0.990 1.030 1.060 1.090 1.100
16.60 16.90 17.10 17.50 17.60 17.80 17.90 18.00 18.30 18.60 19.00 19.20 19.70 19.80 19.70 19.50 19.30 19.10 18.50 17.80 17.60 17.40 17.30 17.10
0.2 0.5 0.7 1.1 1.2 1.4 1.5 1.6 1.9 2.2 2.6 2.8 3.3 3.4 3.3 3.1 2.9 2.7 2.1 1.4 1.2 1.0 0.9 0.7
0.610 0.650 0.700 0.735 0.746 0.758 0.769 0.780 0.790 0.806 0.820 0.830 0.850 0.860 0.870 0.880 0.890 0.900 0.940 0.990 1.030 1.060 1.090 1.100
17.30 17.60 18.10 18.70 19.00 19.30 19.40 19.50 19.90 20.30 20.70 21.10 21.30 21.40 21.30 21.10 20.90 20.70 19.90 19.40 18.70 18.40 18.30 17.80
0.90 1.20 1.70 2.30 2.60 2.90 3.00 3.10 3.50 3.90 4.30 4.70 4.90 5.00 4.90 4.70 4.50 4.30 3.50 3.00 2.30 2.00 1.90 1.40
Bold fonts are used to specify the resonant frequency results.
Table 5 Comparison of frequencies of TLCD system. Analyticala (Hz)
Experimental (Hz)
Difference (%)
0.799
0.860
7.01
a
This value is calculated from Eq. (3).
Table 6 Damping ratios and head-loss coefficients of TLCD system. 4 mm amplitude
8 mm amplitude
Ymax (cm)
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
d
Ymax (cm)
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
d
3.4
0.81
0.92
0.86
6.39
5.2
5.0
0.79
0.94
0.86
8.72
4.81
3.3. Structure-TLCD coupled system and its dynamic characteristics TLCD is installed onto the model structure with four clamps located on the corners to show TLCD’s effect on its dynamic response. In FE model of this coupled system, the masses of TLCD and water are added to that of the structure. FE analysis results are presented in Table 7 for the first three vibration modes. As can be seen, the first three natural frequencies of the coupled system are obtained between 1.547 Hz and 14.533 Hz. According to this result, the resonant frequency of the couple system is specified as 1.55 Hz. As seen, the use of TLCD on the structure reduces the resonant frequency from 2.61 Hz to 1.55 Hz that means 40.6% reduction. Main reason of this reduction is increase in the total mass of the system. Mode shapes are obtained similar to those of the structure without TLCD given by Fig. 4. According to the numerical results given in Tables 1 and 7, 1st natural frequency decreases after TLCD installation onto the structure while higher frequencies increase. However, there is no change in the mass participation ratios for both cases. Table 7 Dynamic characteristics of the coupled system obtained by FEM. Mode number
Period (s)
Frequency (Hz)
Mass participation ratio (%)
1 2 3
0.646 0.108 0.069
1.547 9.276 14.533
87.6 94.0 98.0
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Fig. 10. The coupled system.
Fig. 11. Response time-histories for the resonant frequency, and the maximum amplitude-frequency ratio diagram for 1 mm amplitude and 0° excitation direction.
For shaking table tests of the coupled system, a TLCD with 16.4 cm water level is attached to the top plate of the structure shown in Fig. 10. The coupled system is vibrated on the shaking table using 1 mm and 2 mm source amplitudes between 1.0 Hz and 2.0 Hz frequencies with an increment of 0.1 Hz. Two sensitive accelerometers are used during the measurements,
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Table 8 Dynamic characteristics of the coupled system for the resonant frequency. Amplitude (mm)
1
Damping ratio
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
0.974
1.053
1
3.95
Max Accel. (g)
Max. Vel. (cm/s)
Max. Disp. (mm)
Res. Freq. (Hz)
0.207
21.25
19.69
1.563
Table 9 Damping ratios of the coupled system for different excitation angles. Direction (deg)
1 mm amplitude Max. Accel. (g)
Max. Velocity (cm/sn)
Max. Disp. (mm)
Damping Ratio (%)
Max. Accel. (g)
2 mm amplitude Max. Velocity (cm/sn)
Max. Disp. (mm)
Damping Ratio (%)
0 15 30 45 60 75 90
0.207 0.208 0.166 0.139 0.055 0.050 0.050
21.25 20.36 15.64 12.69 3.80 2.02 1.63
19.69 19.30 14.40 12.18 4.46 1.50 0.77
3.95 4.92 3.83 3.64 3.34 2.70 3.19
0.368 0.415 0.241 0.225 0.105 0.077 0.110
31.95 31.65 23.23 17.64 7.46 3.84 3.37
30.15 28.75 22.39 17.70 7.37 2.89 1.40
4.85 6.34 4.70 5.48 3.59 3.68 2.67
1mm amplitude
2mm amplitude
Fig. 12. Maximum amplitude-frequency ratio diagrams for different excitation angles.
and the collected records are converted by Seismo Signal Software [20] to obtain the velocity and displacement timehistories. The measurements are repeated for excitation directions of 0°, 15°, 30°, 45°, 60°, 75° and 90°. Fig. 11(a and b) shows the acceleration and displacement time histories of resonant frequency (frequency ratio = 1.0) for 1 mm amplitude of the motion with 0°. To calculate the damping ratio, the peak values of displacements are specified, and the amplitudefrequency ratio diagram is formed using the half power bandwidth method as shown in Fig. 11c.
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Fig. 13. Difference (%) between the maximum dynamic responses and damping ratios of the structure with and without TLCD .
Table 8 summarizes the experimental dynamic characteristics of the coupled system in resonant frequency for 1 mm amplitude of the motion with 0°. These calculations are repeated for each excitation directions considering 1 mm and 2 mm amplitudes. Results obtained for the dynamic response are tabulated in Table 9. In addition, the maximum amplitude-frequency ratio diagrams for each amplitude are shown in Fig. 12. According to these figures, response amplitudes are very close to each other for 0° and 15° angles. When the direction changes 0°–90°, the response amplitudes decrease drastically especially for the angles greater than 15°. As previously mentioned, this is expected because the stiffness of the model increases with changing the angles from 0° to 90°. Because of this stiffness change, as seen in Table 9, dynamic responses of the coupled system decrease with increasing the excitation angles. Damping of the system does not show a general trend with changing the motion of direction. To clearly show the effect of TLCD on the structural response, difference percentages in the maximum dynamic responses and damping ratios due to TLCD installation considering the values given in Tables 3 and 9 are presented in Fig. 13. From these figures, we can observe TLCD has significant effect on the accelerations, velocities and damping of the structure for all excitation directions except 90°. Similar trend is also observed for the displacements except the angles greater than 60°. For these angles, measured displacements are so small, and we cannot trust these values due to our test equipment’s capability. For 90° angle, we cannot observe the clear effect of TLCD on the response because the sloshing effect is dominant in this direction instead of the oscillation of water. Fig. 14 also supports these results, which gives comparison of maximum dynamic responses and the damping ratio of the structure with and without TLCD. Fig. 15 shows relation between the frequency and total length of water in TLCD calculated by Eq. (3). As can be seen, there is only one variable (Le ) in this equation which limits its applicability to the structure. According to Fig. 15, TLCD systems
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1mm amplitude
2mm amplitude
Fig. 14. Comparison of the model structure with and without TLCD in terms of the maximum dynamic responses and damping ratios.
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Fig. 15. Relation between the frequency and total length of water in TLCD.
with more than 5 m water length have a frequency within 0.22–0.32 Hz range. To achieve the maximum effectiveness of TLCDs on structural damping, it is necessary to tune the frequency of the structure with TLCD system within this range. 4. Conclusions This study presents experimental evaluation of TLCD effects on the structural responses and damping due ground motions with different excitation directions. For this aim, a steel prototype structure is considered, and its dynamic characteristics with and without TLCD are determined numerically and experimentally. According to the study, the use of TLCD significantly decreases the resonant frequency and dynamic responses of structures. Structural damping increases with TLCD installation. TLCD systems with a water length more than 5 m should be adequate for structures to obtain maximum effectiveness on structural damping. References [1] J. Modal, H. Nimmala, S. Abdulla, R. Tafreshi, Tuned liquid damper, in: Proceedings of the 3rd International Conference on Mechanical Engineering and Mechatronics, Prague, Czech Republic, 2014. [2] E. Sonmez, Nagarajaiah, C. Sun, B. Basu, A study on semi-active tuned liquid column dampers (sTLCDs) for structural response reduction under, J. Sound Vib. 362 (2016) 1–15. [3] F. Sakai, S. Takeda, Tuned liquid column damper-new type device for suppression of building vibrations, in: Proceedings of International Conference on High Rise Buildings, Nanjing, China, 1989. [4] T. Balendra, C.M. Wang, H.F. Cheong, Effectiveness of tuned liquid column dampers for vibration control of towers, Eng. Struct. 17 (9) (1995) 668–675. [5] C.C. Chang, C.T. Hsu, Control performance of liquid column vibration absorbers, Eng. Struct. 20 (7) (1997) 580–586. [6] H. Gao, K.C.S. Kwok, B. Samali, Optimization of tuned liquid column dampers, Eng. Struct. 19 (6) (1997) 476–486. [7] S.K. Yalla, A. Kareem, Semi-active tuned liquid column dampers: experimental study, J. Struct. Eng. 129 (7) (2003) 960–971. [8] J.C. Wu, M.H. Shihb, Y.Y. Lina, Y.C. Shen, Design guidelines for tuned liquid column damper for structures responding to wind, Eng. Struct. 27 (13) (2005) 1893–1905. [9] J.C. Wu, C.H. Chang, Y.Y. Lin, Optimal design for non-uniform tuned liquid column dampers in horizontal motion, J. Sound Vib. 326 (1–2) (2009) 104– 122. [10] P. Chaiviryawong, S. Limkatanyu, T. Pinkaew, Simulations of characteristics of tuned liquid column damper using an elliptical flow path estimation method, in: 14th World Conference on Earthquake Engineering, Beijing, China, 2008. [11] K.A. Al-Saif, K.A. Aldakkan, M.A. Foda, Modified liquid column damper for vibration control of structures, Int. J. Mech. Sci. 53 (7) (2011) 505–512. [12] S.A. Mousavi, S.M. Zahrai, K. Bargi, Optimum geometry of tuned liquid column-gas damper for control of offshore jacket platform vibrations under seismic excitation, Earthq. Eng. Eng. Vib. 11 (4) (2012) 579–592. [13] A. Sarkar, O.T. Gudmestad, Pendulum type liquid column damper (PLCD) for controlling vibrations of a structure: theoretical and experimental study, Eng. Struct. 49 (2013) 221–223. [14] A.F. Mensah, L. Dueñas-Osorio, Improved reliability of wind turbine towers with tuned liquid column dampers (TLCDs), Struct. Saf. 47 (2014) 78–86. [15] Y. Bigdeli, D. Kim, Damping effects of the passive control devices on structural vibration control: TMD, TLC and TLCD for varying total masses, KSCE J. Civ. Eng. 20 (1) (2016) 301–308. [16] H.P. Behbarani, A. Adnan, M. Vafaei, O.P. Pheng, H. Shad, Effects of TLCD with maneuverable flaps on vibration control of a SDOF structure, Meccanica 51 (9) (2016) 1–10. [17] ANSYS, Swanson Analysis System, U.S.A., 2013. [18] PULSE, Analyzers and Solutions, Release 11.2. Bruel and Kjaer, Sound and Vibration Measurement A/S, Denmark, 2006. [19] OMA, Release 4.0, Structural Vibration Solution A/S, Denmark, 2006. [20] Seismo Signal Software, 2016.
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Experimental study on control performance of tuned liquid column dampers considering different excitation directions Ahmet Can Altunisßik ⇑, Ali Yetisßken, Volkan Kahya Karadeniz Technical University, Department of Civil Engineering, Trabzon, Turkey
a r t i c l e
i n f o
Article history: Received 26 October 2016 Received in revised form 17 April 2017 Accepted 15 September 2017
Keywords: Ambient vibration test Damping Dynamic response Ground motion Shaking table Tuned liquid column damper
a b s t r a c t This paper gives experimental tests’ results for the control performance of Tuned Liquid Column Dampers (TLCDs) installed on a prototype structure exposed to ground motions with different directions. The prototype structure designed in the laboratory consists of top and bottom plates with four columns. Finite element analyses and ambient vibration tests are first performed to extract the natural frequencies and mode shapes of the structure. Then, the damping ratio of the structure as well as the resonant frequency, head-loss coefficient, damping ratio, and water height-frequency diagram of the designed TLCD are obtained experimentally by the shaking table tests. To investigate the effect of TLCDs on the structural response, the prototype structure-TLCD coupled system is considered later, and its natural frequencies and related mode shapes are obtained numerically. The acceleration and displacement time-histories are obtained by the shaking table tests to evaluate its damping ratio. To consider different excitation directions, the measurements are repeated for the directions between 0° and 90° with 15° increment. It can be concluded from the study that TLCD causes to decrease the resonant frequency of the structure with increasing of the total mass. Damping ratio considerably increases with installing TLCD on the structure. This is more pronounced for the angles of 0°, 15°, 30° and 45°. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction In structural analyses of high-rise buildings, effect of lateral forces such as wind and earthquake should be evaluated in detail. These buildings may be exposed to the resonant condition under the lateral forces due to the low-frequency content. To avoid harmful effects of the resonant vibrations, the first solution to be considered is to increase the damping capacity of the structure. Seismic isolation, active, passive, semi-active control systems, and other supplemental damping systems are among the various alternatives to reduce the structural vibrations. In active control systems, external power is required to produce the forces to resist the dynamic forces acting on. In passive control systems, dynamic energy is absorbed in the system without any external power supply. Damping and stiffness of semi-active control systems can be controlled during the movement. Semi-active control systems need less energy than active ones. Among the passive control systems, Tuned Liquid Dampers (TLDs) is water confined in a container that uses the sloshing energy of water to reduce the dynamic response of the structure during excitation. TLDs are very effective for absorbing the low-frequency vibrations [1]. As a special case of TLD, Tuned Liquid Column Dampers (TLCDs) having U-shaped tube containing liquid that is usually water has been developed. TLCD can reduce the structural vibrations through the motion of liquid ⇑ Corresponding author at: Karadeniz Technical University, Department of Civil Engineering, 61080 Trabzon, Turkey. E-mail addresses: [email protected] (A.C. Altunisßik), [email protected] (A. Yetisßken), [email protected] (V. Kahya). https://doi.org/10.1016/j.ymssp.2017.09.021 0888-3270/Ó 2017 Elsevier Ltd. All rights reserved.
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residing in the container which counteracts the action of the external excitations [2]. The damping effect of TLCD is produced by the head loss of hydraulic pressure of the liquid due to the orifice installed inside of the container, and the viscous action in the boundary layers. Applications of TLCD on civil engineering structures were first proposed by Sakai and Takeda [3]. Balendra et al. [4] studied on the effectiveness of TLCD for vibration control of towers. Chang and Hsu [5] investigated the control performance of liquid column vibration absorbers for buildings. Gao et al. [6] used a numerical method to account for nonlinearity of the governing equation to determine the effectiveness of TLCD in controlling structural vibrations. Yalla and Kareem [7] performed an experimental study to examine the performance of a prototype semi-active TLCD. Wu et al. [8] proposed the guidelines for industrial practice related to the design of TLCD for damped single-degree-of-freedom structures under wind excitations. Wu et al. [9] summarized the optimal design parameters of TLCD using non-uniform cross-sections in horizontal motion. Chaiviriyawong et al. [10] simulated TLCD using an elliptical flow path estimation method. A modified version of TLCD is proposed by Al-Saif et al. [11] as a passive vibration control device at low-frequencies. Mousavi et al. [12] carried out a detailed investigation on the optimum geometry of tuned liquid column-gas damper for vibrations of an offshore jacket platform under seismic excitations. Sarkar et al. [13] proposed a passive hybrid type damper derived from a pendulum type tuned mass damper and a TLCD. Mensah and Dueñas-Osorio [14] developed a dynamic model of wind turbine to accommodate single/multiple TLCD to control the excessive vibrations. Bigdeli and Kim [15] compared three passive vibration control devices such as Tuned Mass Damper (TMD), TLD and TLCD experimentally. Behbarani et al. [16] showed the effect of TLCD with maneuverable flaps on the vibration control of structures. Ground motions due to earthquakes have three components with different intensities in lateral (longitudinal and transverse) and vertical directions. Almost all design codes suggested the simultaneous implementation of two lateral components such as in x- and y-directions of structures. However, the simultaneous effect of ground motion to whole structure in x- and y-directions is almost impossible. It can be more realistic approach to consider dynamic loads with different directions acting on the structure. This paper presents the experimental tests’ results for the control performance of Tuned Liquid Column Dampers (TLCDs) installed on a prototype structure exposed to ground motions with different directions. For this aim, a prototype structure and a TLCD are designed in the laboratory. They are exposed to the shaking table and ambient vibration tests for obtaining their dynamic characteristics. Finite element analyses are also performed for verification. Different excitation directions are considered by repeating the measurements within 0–90° excitation directions of 15° increment. 2. Analytical background Fig. 1 schematically shows a TLCD model. Equation of motion of liquid surface in TLCD was obtained by Gao et al. [6] with the aid of energy principles associated with the Lagrange’s equations as follows:
€ðtÞ þ y
1 f b €g ðtÞ _ _ þ x20 yðtÞ ¼ x tjyðtÞj yðtÞ 2 Le Le
ð1Þ
€g ðtÞ is the acceleration practiced to TLCD; y €ðtÞ, yðtÞ, _ where x y(t) are the acceleration, velocity and displacement of the liquid inside TLCD, respectively; Av, Ah are the vertical and horizontal cross-sections of TLCD, respectively; t is the cross-section ratio (Av/Ah); f is the damping ratio; x0 is the natural frequency of damper; Le is the total length of liquid in TLCD which can be calculated by
Fig. 1. Configuration of a TLCD system.
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Le ¼ 2h þ tb
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ð2Þ
where h and b are the vertical and horizontal length of liquid columns. The natural frequency of TLCD can be determined by
sffiffiffiffiffiffi 2g x0 ¼ Le
ð3Þ
where g is the acceleration of gravity. 3. Experimental study 3.1. Prototype structure and its dynamic characteristics To evaluate TLCD effects on structural vibrations, a steel prototype structure consists of bottom and top plates and four columns is designed in laboratory. As a support/foundation element, the bottom plate with 300 300 10 mm dimensions is fixed to the shaking table using five bolts, one of them in the middle and others at the edge points. The top plate has 600 600 5 mm dimensions. Four columns, each of which 5 50 1000 mm dimensions, are welded to the top and bottom plates. Because our purpose is also to evaluate the control effectiveness of TLCD under the ground motion with different directions between 0° and 90° with 15° increment, the dimension of bottom plate is restricted, and chosen to be smaller than that of top plate (Fig. 2). Fig. 3 shows the geometric dimensions and laboratory construction models of the prototype structure. To extract natural frequencies and corresponding mode shapes, finite element (FE) model of the structure is constituted in ANSYS Workbench [17]. In FE model, the bottom plate of the structure is assumed to be fixed. The modal analyses are performed under a 244.5N dead load, and natural frequencies and mode shapes are obtained. Fig. 4 shows the FE model and the first mode shape of the structure. In Table 1, the periods, natural frequencies and mass participation ratios are given for the first three modes. For experimental validation, ambient vibration tests are performed on the structure using Operational Modal Analysis (OMA) method. In measurements, B&K3560 data acquisition system with 17 channels and B&K8340 type uni-axial accelerometer are used (Fig. 5). The signals are collected in the data acquisition system, and are transferred into PULSE [18] and OMA [19] software. The dynamic characteristics are extracted using Enhanced Frequency Domain Decomposition (EFDD) method in frequency domain and Stochastic Subspace Identification (SSI) method in time domain. Singular values of the spectral density matrices (SVDSM) of data set and the average of auto spectral densities (AASD) obtained from the EFDD method, as well as the stabilization diagram of estimated state of space model obtained from the SSI method are given Fig. 6. Comparison of numerically and experimentally obtained natural frequencies is given in Table 2. According to the FE analyses and experimental measurements, the resonant frequency of the structure is determined to be 2.61 Hz. To determine the damping ratio of the model structure, experimental studies are performed by using the shaking table with 500 500 mm dimensions, 500N weight and 1000N shaking capacity up to 1 g acceleration. Harmonic sinus waves are applied to the structure on the shaking table in resonant frequency with 1 mm and 2 mm amplitudes during 20 cycles. The time-histories of accelerations are measured from the harmonic vibration using two sensitive accelerometers located on the top and bottom plates of the structure. Butterworth-Bandpass technique is used in all data to filtrations of machine vibrations, and the frequencies between 0.1 Hz and 25 Hz are ignored. Logarithmic Decrement Method are used to calculate the damping ratios for different directions of motion between 0° and 90° with 15° increment. Five different measurements are taken for each case, and the averages of the measurements are used to determine the damping ratios. In addition, the maximum accelerations, velocities and displacements are calculated. Table 3 presents the maximum accelerations, velocities, and displacements, and the damping ratios of the structure for 1 mm and 2 mm amplitudes considering all cases. From this table, we can see that the structural responses decrease when the excitation direction changes from 0° to 90°. This is expected because stiffness of the columns becomes higher when increasing the direction from 0° to 90°. The damping ratios are slightly changed with changing the direction of motion except 90° direction. This is because the displacements for 90° angle are very small, and the calculation of damping ratio becomes difficult. 3.2. Tuned liquid column damper (TLCD) and its dynamic characteristics Before installing to the prototype structure, some structural properties of TLCD such as the resonant frequency, head-loss coefficient, damping ratio and water height-frequency diagram are determined experimentally by the shaking table test. Fig. 7 shows the geometrical properties of TLCD that is constructed by glass material glued each other with polysiloxane (silicone). Weight of the designed TLCD is 130.75N. The amplitude of excitation in harmonic tests is limited to allowable displacement of the structure and the water level in columns such that neither water surface falls below the horizontal portion of TLCD nor water pours out of the columns. TLCD is installed on the shaking table with the aid of four clamps. During the measurements, water heights are read by camera via rulers glued to the surface of glasses. Fig. 8 shows some view of TLCD on the shaking table before the measurements.
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Fig. 2. Dimensions of the bottom plate (units are in mm).
The experimental measurements are conducted using 16.4 cm initial water height (h) for 4 mm and 8 mm amplitudes, respectively. The maximum water heights are observed to be 19.8 cm and 21.4 cm at the frequency of 0.86 Hz for 4 mm and 8 mm amplitudes, respectively. According to this result, we can accept the resonant frequency of TLCD as 0.86 Hz. In Table 5, comparison of measured and calculated natural frequencies of TLCD is given. As seen, a difference of 7% is there between the natural frequencies measured by the shaking table tests and calculated by Eq. (3). This validates our experimental measurements. Fig. 9 presents Dh–Frequency diagram, which is plotted using data between 0.6 Hz and 1.1 Hz given in Table 4. As can be seen from Fig. 9 that maximum increases in water levels are 3.4 cm and 5.0 cm for 4 mm and 8 mm amplitudes, respectively. pffiffiffi The damping ratios are calculated by the half-power bandwidth method. Here, Y max = 2 point is marked on Y axis (see Fig. 9), and frequency ratios (x1 and x2) are then read on X axis. Damping ratios (n) for two different amplitudes (4 mm and 8 mm) are calculated and given in Table 6. The head-loss coefficients (d) is calculated by [4]
Fig. 3. Some views of the prototype structure.
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1st mode
Model structure
Fig. 4. Finite element model and the first mode shape obtained numerically.
Table 1 Dynamic characteristics of the model structure by the finite element method (FEM). Mode number
Period (s)
Frequency (Hz)
Mass participation ratio (%)
1 2 3
0.378 0.133 0.132
2.633 7.548 7.573
87.6 94.0 98.0
Fig. 5. Some views from the measurements and related equipment.
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a) Singular values of spectral density matrices of data set
b) Average of auto spectral densities of data set
c) Stabilization diagram of estimated state of space model Fig. 6. EFDD and SSI results.
Table 2 Comparison of the natural frequencies obtained by FEM and OMA. Mode number
FEM
1 2 3
2.633 7.548 7.573
pffiffiffiffi d ¼ 2L p
f
EFDD method
SSI method
Frequency (Hz)
Error (%)
Frequency (Hz)
Error (%)
2.596 6.916 8.440
1.40 9.14 10.0
2.613 6.901 8.390
0.76 9.37 9.74
Ymax
using the damping ratios and maximum water heights, and given in Table 6.
ð4Þ
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Table 3 Maximum accelerations, velocities and displacements, and damping ratios of the model structure measured for different excitation directions. Direction (deg)
1 mm amplitude Max. Accel. (g)
Max. Vel. (cm/ sn)
Max. Disp. (mm)
Damping Ratio (%)
Max. Accel. (g)
2 mm amplitude Max. Vel. (cm/ sn)
Max. Disp. (mm)
Damping Ratio (%)
0 15 30 45 60 75 90
1.299 1.281 0.919 0.620 0.278 0.123 0.092
60.740 68.690 54.630 36.540 16.360 5.710 1.419
39.190 47.300 37.490 25.830 1.112 0.560 0.420
0.699 0.499 0.512 0.713 0.405 0.671 3.267
2.292 2.317 1.910 1.358 0.620 0.207 0.111
114.960 121.880 105.310 70.440 34.160 9.730 2.612
76.720 78.560 66.390 42.460 20.330 0.553 0.600
0.739 0.695 0.699 0.450 0.775 0.939 2.577
Fig. 7. Geometrical properties of the designed TLCD (units in mm).
Fig. 8. Some view of TLCD system on shaking table before the measurements.
Fig. 9. Dh–frequency diagram for 4 mm and 8 mm amplitudes.
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Table 4 Change of the maximum water heights with frequencies in TLCD system. 4 mm amplitude
8 mm amplitude
Frequency (Hz)
Measured height (cm)
Dh (cm)
Frequency (Hz)
Measured height (cm)
Dh (cm)
0.610 0.650 0.700 0.735 0.746 0.758 0.769 0.780 0.790 0.806 0.820 0.830 0.850 0.860 0.870 0.880 0.890 0.900 0.940 0.990 1.030 1.060 1.090 1.100
16.60 16.90 17.10 17.50 17.60 17.80 17.90 18.00 18.30 18.60 19.00 19.20 19.70 19.80 19.70 19.50 19.30 19.10 18.50 17.80 17.60 17.40 17.30 17.10
0.2 0.5 0.7 1.1 1.2 1.4 1.5 1.6 1.9 2.2 2.6 2.8 3.3 3.4 3.3 3.1 2.9 2.7 2.1 1.4 1.2 1.0 0.9 0.7
0.610 0.650 0.700 0.735 0.746 0.758 0.769 0.780 0.790 0.806 0.820 0.830 0.850 0.860 0.870 0.880 0.890 0.900 0.940 0.990 1.030 1.060 1.090 1.100
17.30 17.60 18.10 18.70 19.00 19.30 19.40 19.50 19.90 20.30 20.70 21.10 21.30 21.40 21.30 21.10 20.90 20.70 19.90 19.40 18.70 18.40 18.30 17.80
0.90 1.20 1.70 2.30 2.60 2.90 3.00 3.10 3.50 3.90 4.30 4.70 4.90 5.00 4.90 4.70 4.50 4.30 3.50 3.00 2.30 2.00 1.90 1.40
Bold fonts are used to specify the resonant frequency results.
Table 5 Comparison of frequencies of TLCD system. Analyticala (Hz)
Experimental (Hz)
Difference (%)
0.799
0.860
7.01
a
This value is calculated from Eq. (3).
Table 6 Damping ratios and head-loss coefficients of TLCD system. 4 mm amplitude
8 mm amplitude
Ymax (cm)
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
d
Ymax (cm)
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
d
3.4
0.81
0.92
0.86
6.39
5.2
5.0
0.79
0.94
0.86
8.72
4.81
3.3. Structure-TLCD coupled system and its dynamic characteristics TLCD is installed onto the model structure with four clamps located on the corners to show TLCD’s effect on its dynamic response. In FE model of this coupled system, the masses of TLCD and water are added to that of the structure. FE analysis results are presented in Table 7 for the first three vibration modes. As can be seen, the first three natural frequencies of the coupled system are obtained between 1.547 Hz and 14.533 Hz. According to this result, the resonant frequency of the couple system is specified as 1.55 Hz. As seen, the use of TLCD on the structure reduces the resonant frequency from 2.61 Hz to 1.55 Hz that means 40.6% reduction. Main reason of this reduction is increase in the total mass of the system. Mode shapes are obtained similar to those of the structure without TLCD given by Fig. 4. According to the numerical results given in Tables 1 and 7, 1st natural frequency decreases after TLCD installation onto the structure while higher frequencies increase. However, there is no change in the mass participation ratios for both cases. Table 7 Dynamic characteristics of the coupled system obtained by FEM. Mode number
Period (s)
Frequency (Hz)
Mass participation ratio (%)
1 2 3
0.646 0.108 0.069
1.547 9.276 14.533
87.6 94.0 98.0
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Fig. 10. The coupled system.
Fig. 11. Response time-histories for the resonant frequency, and the maximum amplitude-frequency ratio diagram for 1 mm amplitude and 0° excitation direction.
For shaking table tests of the coupled system, a TLCD with 16.4 cm water level is attached to the top plate of the structure shown in Fig. 10. The coupled system is vibrated on the shaking table using 1 mm and 2 mm source amplitudes between 1.0 Hz and 2.0 Hz frequencies with an increment of 0.1 Hz. Two sensitive accelerometers are used during the measurements,
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Table 8 Dynamic characteristics of the coupled system for the resonant frequency. Amplitude (mm)
1
Damping ratio
x1 (Hz)
x2 (Hz)
xR (Hz)
n (%)
0.974
1.053
1
3.95
Max Accel. (g)
Max. Vel. (cm/s)
Max. Disp. (mm)
Res. Freq. (Hz)
0.207
21.25
19.69
1.563
Table 9 Damping ratios of the coupled system for different excitation angles. Direction (deg)
1 mm amplitude Max. Accel. (g)
Max. Velocity (cm/sn)
Max. Disp. (mm)
Damping Ratio (%)
Max. Accel. (g)
2 mm amplitude Max. Velocity (cm/sn)
Max. Disp. (mm)
Damping Ratio (%)
0 15 30 45 60 75 90
0.207 0.208 0.166 0.139 0.055 0.050 0.050
21.25 20.36 15.64 12.69 3.80 2.02 1.63
19.69 19.30 14.40 12.18 4.46 1.50 0.77
3.95 4.92 3.83 3.64 3.34 2.70 3.19
0.368 0.415 0.241 0.225 0.105 0.077 0.110
31.95 31.65 23.23 17.64 7.46 3.84 3.37
30.15 28.75 22.39 17.70 7.37 2.89 1.40
4.85 6.34 4.70 5.48 3.59 3.68 2.67
1mm amplitude
2mm amplitude
Fig. 12. Maximum amplitude-frequency ratio diagrams for different excitation angles.
and the collected records are converted by Seismo Signal Software [20] to obtain the velocity and displacement timehistories. The measurements are repeated for excitation directions of 0°, 15°, 30°, 45°, 60°, 75° and 90°. Fig. 11(a and b) shows the acceleration and displacement time histories of resonant frequency (frequency ratio = 1.0) for 1 mm amplitude of the motion with 0°. To calculate the damping ratio, the peak values of displacements are specified, and the amplitudefrequency ratio diagram is formed using the half power bandwidth method as shown in Fig. 11c.
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Fig. 13. Difference (%) between the maximum dynamic responses and damping ratios of the structure with and without TLCD .
Table 8 summarizes the experimental dynamic characteristics of the coupled system in resonant frequency for 1 mm amplitude of the motion with 0°. These calculations are repeated for each excitation directions considering 1 mm and 2 mm amplitudes. Results obtained for the dynamic response are tabulated in Table 9. In addition, the maximum amplitude-frequency ratio diagrams for each amplitude are shown in Fig. 12. According to these figures, response amplitudes are very close to each other for 0° and 15° angles. When the direction changes 0°–90°, the response amplitudes decrease drastically especially for the angles greater than 15°. As previously mentioned, this is expected because the stiffness of the model increases with changing the angles from 0° to 90°. Because of this stiffness change, as seen in Table 9, dynamic responses of the coupled system decrease with increasing the excitation angles. Damping of the system does not show a general trend with changing the motion of direction. To clearly show the effect of TLCD on the structural response, difference percentages in the maximum dynamic responses and damping ratios due to TLCD installation considering the values given in Tables 3 and 9 are presented in Fig. 13. From these figures, we can observe TLCD has significant effect on the accelerations, velocities and damping of the structure for all excitation directions except 90°. Similar trend is also observed for the displacements except the angles greater than 60°. For these angles, measured displacements are so small, and we cannot trust these values due to our test equipment’s capability. For 90° angle, we cannot observe the clear effect of TLCD on the response because the sloshing effect is dominant in this direction instead of the oscillation of water. Fig. 14 also supports these results, which gives comparison of maximum dynamic responses and the damping ratio of the structure with and without TLCD. Fig. 15 shows relation between the frequency and total length of water in TLCD calculated by Eq. (3). As can be seen, there is only one variable (Le ) in this equation which limits its applicability to the structure. According to Fig. 15, TLCD systems
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1mm amplitude
2mm amplitude
Fig. 14. Comparison of the model structure with and without TLCD in terms of the maximum dynamic responses and damping ratios.
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Fig. 15. Relation between the frequency and total length of water in TLCD.
with more than 5 m water length have a frequency within 0.22–0.32 Hz range. To achieve the maximum effectiveness of TLCDs on structural damping, it is necessary to tune the frequency of the structure with TLCD system within this range. 4. Conclusions This study presents experimental evaluation of TLCD effects on the structural responses and damping due ground motions with different excitation directions. For this aim, a steel prototype structure is considered, and its dynamic characteristics with and without TLCD are determined numerically and experimentally. According to the study, the use of TLCD significantly decreases the resonant frequency and dynamic responses of structures. Structural damping increases with TLCD installation. TLCD systems with a water length more than 5 m should be adequate for structures to obtain maximum effectiveness on structural damping. References [1] J. Modal, H. Nimmala, S. Abdulla, R. Tafreshi, Tuned liquid damper, in: Proceedings of the 3rd International Conference on Mechanical Engineering and Mechatronics, Prague, Czech Republic, 2014. [2] E. Sonmez, Nagarajaiah, C. Sun, B. Basu, A study on semi-active tuned liquid column dampers (sTLCDs) for structural response reduction under, J. Sound Vib. 362 (2016) 1–15. [3] F. Sakai, S. Takeda, Tuned liquid column damper-new type device for suppression of building vibrations, in: Proceedings of International Conference on High Rise Buildings, Nanjing, China, 1989. [4] T. Balendra, C.M. Wang, H.F. Cheong, Effectiveness of tuned liquid column dampers for vibration control of towers, Eng. Struct. 17 (9) (1995) 668–675. [5] C.C. Chang, C.T. Hsu, Control performance of liquid column vibration absorbers, Eng. Struct. 20 (7) (1997) 580–586. [6] H. Gao, K.C.S. Kwok, B. Samali, Optimization of tuned liquid column dampers, Eng. Struct. 19 (6) (1997) 476–486. [7] S.K. Yalla, A. Kareem, Semi-active tuned liquid column dampers: experimental study, J. Struct. Eng. 129 (7) (2003) 960–971. [8] J.C. Wu, M.H. Shihb, Y.Y. Lina, Y.C. Shen, Design guidelines for tuned liquid column damper for structures responding to wind, Eng. Struct. 27 (13) (2005) 1893–1905. [9] J.C. Wu, C.H. Chang, Y.Y. Lin, Optimal design for non-uniform tuned liquid column dampers in horizontal motion, J. Sound Vib. 326 (1–2) (2009) 104– 122. [10] P. Chaiviryawong, S. Limkatanyu, T. Pinkaew, Simulations of characteristics of tuned liquid column damper using an elliptical flow path estimation method, in: 14th World Conference on Earthquake Engineering, Beijing, China, 2008. [11] K.A. Al-Saif, K.A. Aldakkan, M.A. Foda, Modified liquid column damper for vibration control of structures, Int. J. Mech. Sci. 53 (7) (2011) 505–512. [12] S.A. Mousavi, S.M. Zahrai, K. Bargi, Optimum geometry of tuned liquid column-gas damper for control of offshore jacket platform vibrations under seismic excitation, Earthq. Eng. Eng. Vib. 11 (4) (2012) 579–592. [13] A. Sarkar, O.T. Gudmestad, Pendulum type liquid column damper (PLCD) for controlling vibrations of a structure: theoretical and experimental study, Eng. Struct. 49 (2013) 221–223. [14] A.F. Mensah, L. Dueñas-Osorio, Improved reliability of wind turbine towers with tuned liquid column dampers (TLCDs), Struct. Saf. 47 (2014) 78–86. [15] Y. Bigdeli, D. Kim, Damping effects of the passive control devices on structural vibration control: TMD, TLC and TLCD for varying total masses, KSCE J. Civ. Eng. 20 (1) (2016) 301–308. [16] H.P. Behbarani, A. Adnan, M. Vafaei, O.P. Pheng, H. Shad, Effects of TLCD with maneuverable flaps on vibration control of a SDOF structure, Meccanica 51 (9) (2016) 1–10. [17] ANSYS, Swanson Analysis System, U.S.A., 2013. [18] PULSE, Analyzers and Solutions, Release 11.2. Bruel and Kjaer, Sound and Vibration Measurement A/S, Denmark, 2006. [19] OMA, Release 4.0, Structural Vibration Solution A/S, Denmark, 2006. [20] Seismo Signal Software, 2016.