DYNAMIC TEST OF MULTIPLE TUNED MASS DAMPERS FOR VIBRATION CONTROL OF HIGH-RISE BUILDINGS

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1 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaa DYNAMIC TEST OF MULTIPLE TUNED MASS DAMPERS FOR VIBRATION CONTROL OF HIGH-RISE BUILDINGS C. C. Lin 1, G. L. Lin 2 and H. Y. Lung 3 ABSTRACT A multiple tuned mass dampers (MTMD) system consists of multiple units of tuned mass dampers (TMDs) arranged in parallel to suppress vibrations of single or multiple modes of structural responses. This proposed control device creates a broader bandwidth than conventional single TMD, and thus, mitigates the frequency detuning problem by taking into account the variation of controlled structural frequency. In recent decade, lots of high-rise buildings have been implemented with TMD devices. To control such a long period structure needs to use a TMD system with long stroke. In this study, an MTMD system with long stroke has been developed for vibration control of high-rise buildings. A sliding typed MTMD system composed of three units of TMD arranged in parallel was fabricated. A series of shaking table tests were conducted to verify the dynamic properties of the MTMD system. Test items include the identifications of frequency of each TMD unit and friction coefficient (or equivalent damping ratio), noise during MTMD movement and fail/safe lock mechanism. The results of shaking table tests demonstrate that experimental results agree well with the theoretical results, and the fail/safe device has satisfactory performance. The identified MTMD parameters were used for the control of a target building through numerical simulation to evaluate its control performance. 1 Distinguished Professor, 2 Post-Doctoral Research Fellow, 3 Graduate student, Department of Civil Engineering, National Chung Hsing University, 25 Kuo-Kuang Road, Taichung 4227, Taiwan.

2 Dynamic Test of Multiple Tuned Mass Dampers for Vibration Control of High-Rise Buildings C. C. Lin 1, G. L. Lin 2, and H. Y. Lung 3 ABSTRACT A multiple tuned mass dampers (MTMD) system consists of multiple units of tuned mass dampers (TMDs) arranged in parallel to suppress vibrations of single or multiple modes of structural responses. This proposed control device creates a broader bandwidth than conventional single TMD, and thus, mitigates the frequency detuning problem by taking into account the variation of controlled structural frequency. In recent decade, lots of high-rise buildings have been implemented with TMD devices. To control such a long period structure needs to use a TMD system with long stroke. In this study, an MTMD system with long stroke has been developed for vibration control of high-rise buildings. A sliding typed MTMD system composed of three units of TMD arranged in parallel was fabricated. A series of shaking table tests were conducted to verify the dynamic properties of the MTMD system. Test items include the identifications of frequency of each TMD unit and friction coefficient (or equivalent damping ratio), noise during MTMD movement and fail/safe lock mechanism. The results of shaking table tests demonstrate that experimental results agree well with the theoretical results, and the fail/safe device has satisfactory performance. The identified MTMD parameters were used for the control of a target building through numerical simulation to evaluate its control performance. Introduction Vibration control of structures using supplemental devices against natural and man-made excitations has been a topic of interest in civil engineering in recent decades. Among those devices, tuned mass damper (TMD) is one kind of passive-type devices and can be incorporated into an existing structure with less interference compared with others. The design concept and procedure for tuned mass dampers (TMDs) have been extensively investigated through numerical simulation analyses and experimental tests. Sophisticated three-dimensional building models were developed to examine the optimum installation location in elevation and in plane, number and movement direction of the TMDs with the consideration of translation-torsion coupling and soil-structure interaction effects. Analytical and empirical formulas were also derived to determine the optimal parameters of TMD [1]. Since 1975, TMDs have been successfully installed in high-rise buildings, observatory towers, 1 Distinguished Professor, 2 Post-Doctoral Research Fellow,. 3 Graduate student, Department of Civil Engineering, National Chung Hsing University, 25 Kuo-Kuang Road, Taichung 4227, Taiwan.

3 building floors, and pedestrian bridges. All of these applications showed that TMDs can considerably reduce structural vibrations. However, a TMD could face some drawbacks in seismic applications, such as large stroke and detuning problem, due to large earthquake forces. To solve the detuning problem, multiple tuned mass dampers (MTMDs) composed of multiple units of TMD were proposed [2]. Through numerous studies [3-15] in recent years, various design theories and control procedure of an MTMD system were developed. It is generally recognized that TMD s performance relies on its large stroke which may not be allowed due to the limitations of moving space and system components. In 21, a novel MTMD s design theory with the consideration of stroke limitation was proposed by Lin et al. [16, 17]. A series of shaking table tests were also conducted to verify the control effectiveness of a five-unit MTMD device for a large-scale three-story benchmark building at the National Center for Research on Earthquake Engineering (NCREE) in Taiwan. In recent decade, lots of high-rise buildings have been implemented with TMD control devices. To control such a long period structure, a TMD system with long stroke is required. In this study, an MTMD system with long stroke has been developed for vibration control of high-rise buildings. A sliding typed MTMD system composed of three units of TMD arranged in parallel was fabricated. A series of shaking table tests were conducted to verify the dynamic properties of the MTMD system. Test items include the identifications of frequency of each TMD unit and friction coefficient (or equivalent damping ratio), noise during MTMD movement and fail/safe lock mechanism. The identified MTMD parameters were used for the control of a target building through numerical simulation to evaluate its control performance. Design and Fabrication of a Long Stroke MTMD Optimal MTMD s Parameters for the Target Building A symmetric building is selected as the target building, which is a 38-story building located in Taipei, Taiwan. Based on the design drawings of the target building, the commercial finite element program ETABS was employed to calculate modal parameters of the target building, as shown in Table 1. The fundamental period of the target building is 3.64 second along the Y (weak) direction. According to the dynamic properties of the target building, a three-unit MTMD system with total weight of 5 tonf is designed to control the vibration in weak direction. Table 2 shows the optimal MTMD s parameters obtained by using the optimal design method. The mass ratio of the MTMD system is.144% to the total weight of the building. Each MTMD s unit has identical stiffness coefficient and damping coefficient to save the construction cost. The frequency of each TMD unit is.26 Hz,.27 Hz, and.28 Hz, respectively. The fundamental modal damping ratio of the target building can be increased from 1.% to 2.65 %, by using the MTMD as shown in Table 1. Fabrication of Scale-down MTMD System To control a long period target building needs to use a TMD system with long stroke. In this study, the stroke of each MTMD unit is designed as 5cm. Because of both limitations of budget and test facility, the total weight of the MTMD system is reduced to be 5 kgf (1/1 scaled

down), as shown in Table 3. Fig. 1 shows the schematic diagram of the MTMD system consisting of three TMD units.

The mass block is rested on a linear guide rail system, which consists of four sliding blocks and two guide rails, as shown in Fig. 3.

Two shock absorbers and rubber buffers are provided at both sides to prevent damage of the TMD unit, as shown in Fig. 4.

4 down), as shown in Table 3. Fig. 1 shows the schematic diagram of the MTMD system consisting of three TMD units. Each TMD unit is composed of a mass block and two precompression springs, as shown in Fig. 2. A steel tube passes through the springs to prevent them from buckling. The mass block is rested on a linear guide rail system, which consists of four sliding blocks and two guide rails, as shown in Fig. 3. Friction between the sliding blocks and guide rails provides damping of each TMD unit. Because of the existence of the springs, each TMD unit has a constant tuning frequency. Two shock absorbers and rubber buffers are provided at both sides to prevent damage of the TMD unit, as shown in Fig. 4. Moreover, a fail/safe system consists of two hooks and one rod is designed to lock the TMD unit for allo of the unexpected severe excitations. The hook mounted at the location of maxima stroke while the rod mounted at the mass block, as shown in Fig.5. When TMD s stroke exceeds its limit (5cm), the mass block will be locked for safety. Fig. 6 shows the completely fabricated MTMD system. Table 1. Parameters of target building Target Building Total floors (F) 38 Control direction Y (weak direction) Total weight of building (Tonf) 34,624.6 Modal effective mass (Tonf) 25,641. Natural period (sec.) 3.64 Modal damping ratio (w/o MTMD) (%) 1. Modal damping ratio (w/ MTMD) (%) 2.65 Table 2. Parameters of target building and MTMD system. MTMD system Mass ratio (%).144 Modal mass ratio (%).195 Total weight of MTMD (Tonf) 5 Installation location of MTMD (F) 36 MTMD1 MTMD2 MTMD3 Weight (Tonf) Stiffness (kn/m) Damping coefficient (kn-sec/m) Damping ratio (%) 1.41% 1.45% 1.5% Period (sec.) Frequency (Hz) Table 3. Ideal parameters of scale-down MTMD system. MTMD Unit #1 #2 #3 Weight (kgf) Frequency (Hz) Damping ratio Figure 1. Schematic diagram of the MTMD.

(a) Slide block (b) Guide rails Figure 3.

experimentally, seismic responses of the

and one accelerometer were placed upon both

5 (a) Mass block (b) Compression spring Figure 2. Mass block and compression spring. (a) Slide block (b) Guide rails Figure 3. Sliding block and guide rails. Figure 4. Shock absorbers and rubber buffers. (a) Hook Figure 5. Fail/safe device. (b) Rod Figure 6. Fabricated MTMD. Shaking Table Tests Test Setup and Test Items In order to evaluate the dynamic properties of the MTMD system experimentally, seismic responses of the prototype MTMD was investigated through a series of shaking table tests. Fig. 7 depicts the test setup and the sensor placement of the shaking table test. As shown in the figure, one velocity sensor and one accelerometer were placed upon both the shaking table and each TMD unit. In addition, a LVDT was also used to measure the stroke of each TMD unit. Test

6 items include: (1) harmonic test, (2) seismic excitation test, (3) test of fail/safe lock mechanism, and (4) noise test. Results of Harmonic Test Due to manufacturing error, the stiffness of each spring is not ideally identical. Therefore, the real frequency of each TMD unit should be calibrated. To make sure the frequency of each TMD unit agrees with the designed value, a cyclic test (excitation amplitude = 7mm, frequency = Hz) has been conducted firstly. By adjusting the mass of each TMD unit, the tuning frequency can be changed. Table 4 lists the results of harmonic test. The peak stroke appears when the excitation frequency is closed to the frequency of each TMD unit. It is found that the frequency of MTMD#1 to MTMD#3 equals to.26hz,.27hz, and.28hz, respectively. Figure 7. Setup of shaking table test. Test of Fail/Safe Lock Mechanism A fail/safe system is designed to lock the TMD unit for safety during a severe excitation. The fail/safe test is adopted via a harmonic excitation (amplitude = 9mm, frequency =.27 Hz). Fig. 8 shows the stroke and acceleration responses of the MTMD#3. It is seen that the MTMD#3 is locked by the device after 31 second of the excitation. After this moment, the TMD s stroke reaches 5cm and its acceleration equals to the excitation. It proves that the fail/safe device works well. 1 Stroke (MTMD #3) Absolute acc. (MTMD #3).5 (31sec,.5m) lock stop 2 1 (31sec) lock stop Stroke (m) Acc. (m/s 2 ) Time (sec) (a) Stroke Time (sec) (b) Acceleration Figure 8. Time histories of the fail/safe device test.

7 Test of Movement Noise Since the target building is a residential building, noise induced by the movement of MTMD system should be considered to assure the living quality of the building. The movement noise mainly results from the friction of the guide rail system and the friction between the spring and steel tube. The noise at different distances was measured as given in Table 5. Compared with the background noise, it shows that the movement noise level of the MTMD system is small and acceptable. Table 4. Results of harmonic test. Table 5. Results of movement noise test. Sine MTMD#1 MTMD#2 MTMD#3 Hz Max. stroke (mm) Distance db (w/o movement) db (w/ movement) 1m m m Comparison of and Harmonic and Seismic Responses In order to ensure the accuracy of the experiment, the test data was compared with the theoretical results simulated by using a Coulomb-friction model [18-2], as shown in Fig. 9. The simulated acceleration signals measured at the shaking table are regarded as the input ground excitations. Table 6 lists the identified system parameters of the MTMD system. It is noted that the total weight of the MTMD is 591. kg, which is larger than the design value due to manufacturing error of the springs. Fig. 1 compares the experimental with simulated responses of the MTMD system subjected to 194 El Centro earthquake excitation (PGA = 4gal). It must be pointed out that the total shear force S k (t) of the k-th TMD unit shown in these figures are reconstructed from the test data. The computation of shear force S k (t) and friction force F k (t) is explained below. Since each TMD unit is a rigid mass block, from the dynamic equilibrium equation, the total shear force S k (t) of each TMD unit can be written as S ( t) = F ( t) + k v ( t) = m v&, ( t) (1) k k where & ( ) and F k (t) denote the absolute acceleration and indicates the friction force of the k- v&, a t th TMD unit, respectively. Since & ( ) and v (t) are measured and available, F k (t) can be computed by the following equation v&, a t a F ( t) = k v ( t) m v&, ( t) (2) k a

8 In addition, the friction force F k (t) of the TMD unit can be further written as F ( t) = sgn( v& ( t)) m g (3) k µ k where the function sgn( v& ( t)) denotes the sign of v& (t). Then, the friction coefficient µ k can be estimated by Eq. (2) and Eq. (3). From Fig 1, the following observations can be made: (1) generally speaking, regardless of type of excitations, the MTMD dynamic behaviors predicted by the theoretical model are all very good agreement with the measured data This indicates that the test data are reliable and the MTMD dynamic responses can be obtained by the proposed analytical methods. (2) Due to the complicated friction behavior as well as measurement noise, the experimental and theoretical hysteresis loops of the TMD unit have a relatively large but acceptable discrepancy (see Fig 1(c)), as compared to the other system responses. In addition, this discrepancy does not affect the responses of the MTMD, because both the stroke and acceleration responses predicted by the theoretical model match well with the experimental ones. Fig. 11 compares the peak stroke of each TMD unit for different level of PGAs. The results reveal that the dynamic behavior of the MTMD system is predictable by the Coulomb-friction model. Table 6. Identified parameters of the MTMD system. MTMD#1 MTMD#2 MTMD#3 Weight (kgf) Frequency (Hz) Friction coefficient Figure 9. Coulomb-friction model. In order to verify the control efficiency of the MTMD system, the dynamic behaviors of target building with and without the MTMD system are simulated via critical parameters that identified from the shaking table test. For simplicity, a linearization is applied to calculate the equivalent viscous damping ratio of each TMD unit. It is noted that: (1) the friction coefficient of the fullscale MTMD system remains.16, which is a reasonable value for a TMD unit supported by a linear guide-rail system; (2) to tune the frequency of each TMD unit correctly, total mass ratio of the MTMD system is larger than that of the design value due to manufacturing error of the springs. Because of this reason, the equivalent damping ratio of the target building equipped with the MTMD system based on the experimental parameters is 2.73%, which is larger than the desired value of 2.65%. Fig. 12 compares the control performance of MTMD systems based on the designed and experimental parameters. The experimental MTMD system performs better than that as desired.

9 Stroke (m) Stroke (MTMD #3) Acc. (m/s 2 ) Absolute acc (MTMD #3) Time (sec) (a) Stroke 15 1 Total hysteretic loop (MTMD #3) Time (sec) (b) Acceleration Total shear (N) Stroke (m) (c) Hysteresis loop Figure 1. Seismic responses of MTMD#3 (El Centro, PGA=4gal) Max. Stroke (MTMD #1).25.2 Max. Stroke (MTMD #2) Stroke (m).15.1 Stroke (m) PGA (gal) (a) MTMD# Max. Stroke (MTMD #3) PGA (gal) (b) MTMD#2 Stroke (m) PGA (gal) (c) MTMD#3 Figure 11. Seismic responses of MTMD with respect to different PGAs

10 5 4 w/o w/ w/ H(w) Frequency Figure 12. Control performances of the MTMD systems with experimental and theoretical parameters. Conclusions A long-stroke MTMD system composed of three TMD units has been designed and fabricated in this study to reduce the vibration of a high-rise building. The dynamic properties of the MTMD system are verified experimentally by shaking table tests. The test items include frequency of each MTMD unit and friction coefficient (or equivalent damping ratio), noise during MTMD movement and fail/safe lock mechanism. The dynamic behaviors of the prototype MTMD system were also simulated and verified by the developed theoretical model. The shaking table test results demonstrate that experimental results agree well with the theoretical results, which indicate the dynamic behavior of the MTMD system is predictable. In addition, the fail/safe device works well when the stroke exceeds its limit while the noise test shows the movement noise of the MTMD system is acceptable. Finally, the identified MTMD parameters were used for the vibration control of the target building. The results of numerical simulation show that the control performance of the MTMD system performs well as desired. Acknowledgments This research is sponsored in part by the National Science Council and the National Center for Research on Earthquake Engineering, Taiwan, R.O.C., through the grant NSC E5-5-CC2. This sponsorship is gratefully acknowledged. The authors also appreciate the China Steel Structure Co., Ltd. in Taiwan for fabrication of the MTMD system. References 1. Lin CC, Wang JF. Optimal Design and Practical Considerations of Tuned Mass Dampers for Structural Control, chapter 6 in Design Optimization of Active and Passive Structural Control Systems, IGI Global Publisher, Xu K, Igusa T. Dynamic characteristics of multiple substructures with closely spaced frequencies. Earthquake Engineering and Structural Dynamics 1992; 21(12): Yamaguchi H, Harnpornchai N. Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations. Earthquake Engineering and Structural Dynamics 1993; 22:

11 4. Abe M, Fujino Y. Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthquake Engineering and Structural Dynamics 1994; 23: Abe M, Igusa T. Tuned mass dampers for structures with closely spaced natural frequencies. Earthquake Engineering and Structural Dynamics 1995; 24: Jangid RS. Dynamic characteristics of structures with multiple tuned mass dampers. Structural Engineering and Mechanics 1995; 3: Lin CC, Ueng JM, Huang TC. Seismic response reduction of irregular buildings using passive tuned mass dampers. Engineering Structures 1999, 22(5): Li C. Performance of multiple tuned mass fampers for attenuating undesirable oscillations of structures under the ground acceleration. Earthquake Engineering and Structural Dynamics 2; 29: Li C. Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF. Earthquake Engineering and Structural Dynamics 22; 31: Li C, Liu Y. Optimum multiple tuned mass dampers for structures under the ground acceleration based on the uniform distribution of system parameters. Earthquake Engineering and Structural Dynamics 23; 32: Lin CC, Wang JF, Chen BL. Train-induced vibration control of high-speed railway bridges equipped with multiple tuned mass dampers. Journal of Bridge Engineering (ASCE) 25; 1(4): Wang JF, Lin CC. Seismic performance of multiple tuned mass dampers for soil-irregular building interaction systems. International Journal of Solids and Structures 25; 42(2): Hoang N, Warnitchai P. Design of multiple tuned mass dampers by using a numerical optimizer. Earthquake Engineering and Structural Dynamics 25; 34: Zuo L, Nayfeh SA. Optimization of the individual stiffness and damping parameters in multiple-tuned-massdamper system. Journal of Vibration and Acoustics (ASME) 25; 127(1): Li H, Ni X. Optimization of non-uniformly distributed multiple tuned mass damper. Journal of Sound and Vibration 27; 38: Wang JF, Lin CC, Lian CH. Two-stage optimum design of tuned mass dampers with consideration of stroke. Structural Control and Health Monitoring 29; 16: Lin CC, Wang JF, Lien CH, Chiang HW, Lin CS. Optimum design and experimental study of multiple tuned mass dampers with limited stroke. Earthquake Engineering and Structural Dynamics 21; 39: Lu LY, Chung LL, Wu LY, Lin GL. Dynamic analysis of structures with friction devices using discrete-time state-space formulation. Computers and Structures 26; 84(15-16): Lin CC, Lin GL, Wang JF. Protection of seismic structures using semi-active friction TMD. Earthquake Engineering and Structural Dynamics 21; 39(6): Lin GL, Lin CC, Lu LY, Ho YB. verification of seismic vibration control using a semi-active friction tuned mass damper. Earthquake Engineering and Structural Dynamics 212; 41(4):

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