PERFORMANCE OF TUNED MASS DAMPERS FOR RESPONSE REDUCTION OF STRUCTURES UNDER NEAR-FIELD AND FAR-FIELD SEISMIC EXCITATIONS

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1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 112 PERFORMANCE OF TUNED MASS DAMPERS FOR RESPONSE REDUCTION OF STRUCTURES UNDER NEAR-FIELD AND FAR-FIELD SEISMIC EXCITATIONS Babak Kamrani-Moghaddam 1, Mohammad Rahimian 2 and Amir K. Ghorbani-Tanha 3 ABSTRACT The performance of using tuned mass dampers (TMDs) in response reduction of structures for nearfield and far-field earthquakes is investigated. The 3-, 9- and 20- story structures that designed for SAC phase II project are used in this study. First, time history analyses are performed to calculate the response of each structure subjected to Chi-Chi, Kocaeili and Landers near-field and far-field earthquake records. The same procedure followed for models with attached TMD. The results show that the performance of TMD in 3- story structure is better for far-field structure while for 20- story structure the performance is better for near-field excitations. Keywords: Tuned Mass Damper, Near-Field Earthquake, Far-Field Earthquake INTRODUCTION A tuned mass damper (TMD) is a passive energy dissipation device, consists of a mass, spring and a viscous damper, attached to the structure and improves the response of structure induced by winds or earthquake loads. TMD first introduced by Fahrm in 1909 (Housner et al., 1997; Soong and Dargush,1997). TMD has been successfully used in structures to improve the wind-induced vibrations; such as CN Tower in Canada, John Hancock Building in Boston, Center-Point Tower in Sydney, and the Taipei 101 Tower in Taiwan, the tallest building in the world and extensive studies have been conducted by researchers to investigate the performance of TMDs in response improvement of structures under seismic loads (e.g., Den Hartog, 1956; McNamara, 1977; Warburton, 1982; Kwok, 1984, Sadek et al., 1997; Wang and Fung, 2000; Wong and Chee, 2004, Lee et al., 2006). During an earthquake, in the near-fault zone, ground motion properties can be different and are influenced by some phenomena such as rupture mechanism, direction of rupture propagation relative to the site and permanent ground displacements resulting from the fault slip. Therefore recorded near field acceleration time histories have different properties such as higher frequency and long period vibrations and structures will be respond differently to them (Kramer, 2005). It appears that performed studies on performance of TMDs for response reduction of structures under near-field and far-field seismic excitations are very limited. In this paper, performance of TMDs for response reduction of structures under near-field and far-field seismic excitations is investigated. Three 3-, 9-, and 20-story structures which designed for SAC phase 1 MSc Student of Civil-Earthquake Engineering, School of Civil Engineering, University of Tehran, Tehran, Iran, babakkamrani@yahoo.com 2 Associate Professor, School of Civil Engineering, University of Tehran, Tehran, Iran, rahimian@ut.ac.ir 3 PhD Candidate, School of Civil Engineering, University of Tehran, Tehran, Iran, ghtanha@ut.ac.ir

2 II project, structures are considered. Analyses are performed for these structures, without and with attached TMDs, subjected to Chi-Chi, Kocaeili and Landers near-field and far-field earthquake records. Numerical analyses are performed and the results together with the conclusions are reported. EQUATION OF MOTION The equation of motion for an n degree of freedom structure with an attached TMD to the top floor subjected to earthquake excitation can be written as M& x ( + Cx& ( + Kx ( = Mr u && ( (1) where M, C and K are (n+1) (n+1) mass, damping and stiffness matrices respectively; x( is (n+1) -dimensional displacement vector; u& g ( is the ground acceleration; r is the (n+1) element unit vector and the dot indicates a derivative with respect to time. Eq. (1) can be expressed in state space as (Ogata, 2005) g z & ( = Az ( + B&& u ( (2) where z ( is ( 2n + 2) element state vector; A is ( 2n + 2) (2n + 2) system matrix; B is ( 2n + 2) 1 external excitation location vector, given, respectively, by g x( z( = ; x& ( = 0 I 0 A 1 M K M 1 and B = C (3) r DESCRIPTION OF STRUCTURES AND TMDS USED IN CURRENT STUDY Three 3-, 9-, and 20- story structures are used in this paper. The mass and stiffness of stories are assumed to be similar to those of SAC Phase II Steel Project Buildings (Ohtori et al., 2004). The structures are assumed to be undamped. The first natural frequency of the structures are summarized in Table 1. Table 1. The first natural frequency of the structures First Natural Structure Frequency, f n, (Hz) 3-story story story 0.26 Natural properties of each TMD can be obtained by the following relations (Sadek et al., 1997) 1 µ Φ f = 1 β (4) 1+ µ Φ 1+ µ Φ β ξ = Φ + 1+ µ µ 1+ µ (5)

3 where Ф is the amplitude of tuning mode of vibration for a unit modal participation factor computed at the location of TMD; µ is the ratio of the mass of TMD to the generalized mass of the structure in the tuning mode; β is the tuning mode damping ratio; f is the ratio of TMD frequency to that which the mass damper is to be tuned, and ξ is the TMD s damping ratio. A single TMD is connected to the roof of each structure and the analyses for each case is performed. The mass ratio (µ) is assumed to be 0.01 for all structures. GROUND MOTIONS USED The earthquakes used in present study are presented in Table 2. All of them have been recorded on the rock or stiff soil (shear wave velocity>750 m/s). Response spectra of each used records for 5% damping are shown in Figs. 1, 2, and 3. Earthquake Ms Record Chi-Chi, Taiwan 1999/09/20 Kocaeli, Turkey 1999/08/17 Landers 1992/06/28 NF is the abbreviation of Near-Filed * FF is the abbreviation of Far-Field ** Table 2. Earthquake records used Epicentral Distance (km) Station Name and Component NF * TCU046-N FF ** HWA056-W NF 4.8 IZT090 FF 63.9 MSK000 NF 1.1 LCN275 FF 51.7 SIL000 CHI-CHI (Far-Field) CHI-CHI (Near-Field) Pseudo Acceleration (g) Period (sec) Figure 1. Pseudo acceleration response spectra for 5% damping for near-field and far-field Chi-Chi earthquake records. KOCAEILI (Far-Field) KOCAEILI (Near-Field) 1.2 Pseudo Acceleration (g) Period (sec) Figure 2. Pseudo acceleration response spectra for 5% damping for near-field and far-field Kocaeili earthquake records.

4 2.5 LANDERS (Far-Field) LANDERS (Near-Field) Pseudo Acceleration (g) Period (sec) Figure 3. Pseudo acceleration response spectra for 5% damping for near-field and far-field Landers earthquake records. EVALUATION CRITERIA In order to evaluate the performance of the employed control device on structural response improvement, the following non-dimensional evaluation criteria are calculated for each story J 1 d( max t = h max δ and J 2 max && x t = && xa a max ( (6-7) d( max J = h 3 max and J δ 4 max && xa( t = max max && x a (8-9) where d( is the interstory drift for the controlled structure; h is the story height; δ max is the maximum interstory drift ratio of the uncontrolled structure; & x a ( is the story acceleration of controlled structure ; & x& max a is the maximum story acceleration of the uncontrolled structure and the norm,, is calculated from following equation = 1 t f t 0 f [] 2 dt (10) where t f is the duration of the time history of the earthquake used. Small values of the evaluation criteria are more desirable. NUMERICAL RESULTS Numerical analyses are performed and the results for the average of evaluation criteria obtained by undertaking three different earthquake records as the external excitations are shown in Figs Performed analyses show that for 3-story structure, TMD exhibits more efficiency in far-field excitations than near-source ones. Contrary to 3-story structure, in the case of 20-story structure, TMD is generally more efficient in structural response improvement under near-source ground excitations. For 9-story structure, no clear judgment can be made. The overall results show that incorporating a TMD to the structure generally reduces the interstory drifts and acceleration responses. While the reduction of interstory drifts for the lower stories is more than the upper ones, story accelerations are more mitigated in the upper levels.

5 Figure 1. Evaluation Criteria for 3- story building under Chi-Chi earthquake excitation. Figure 2. Evaluation Criteria for 3- story building under Kocaeili earthquake excitation. Figure 3. Evaluation Criteria for 3- story building under Landers earthquake excitation.

6 Figure 4. Evaluation Criteria for 9- story building under Chi-Chi earthquake excitation. Figure 5. Evaluation Criteria for 9- story building under Kocaeili earthquake excitation. Figure 6. Evaluation Criteria for 9- story building under Landers earthquake excitation.

7 Figure 7. Evaluation Criteria for 20- story building under Chi-Chi earthquake excitation. Figure 8. Evaluation Criteria for 20- story building under Kocaeili earthquake excitation. Figure 9. Evaluation Criteria for 20- story building under Landers earthquake excitation.

8 CONCLUSIONS Numerical analyses are conducted to investigate the performance of TMDs for response reduction of structures under near-field and far-field seismic excitations. The results show that, for 3- story structure, TMD exhibits more efficiency in far-field excitations, while for 20- story structure, TMD is generally more efficient in near-field excitations. Overall results show that TMD is more efficient for interstory drift reduction of lower levels and story acceleration reduction of upper levels. ACKNOWLEDGMENTS The authors would like to thank Dr. Asadollah Noorzad, Dr. Abbas Ghalandarzadeh and Mr. Hamid Zafarani for their valuable comments and guidance. REFERENCES Chopra, A.K. (2004). Dynamics of Structures Theory and Applications to Earthquake Engineering, Prentice-Hall of India, New Delhi. Den Hartog, J.P. (1956). Mechanical Vibrations, Mc-Graw Hill Inc., New York, NY. Housner, G.W., L.A. Bergman, T.K. Caughey, A.G. Chassiakos, R.O. Claus, S.F. Masri, R.E. Skelton, T.T. Soong, B.F. Spencer Jr., and J.T.P. Yao (1997). Structural Control: Past, Present and Future, Journal of Engineering Mechanics, 123(9), Kramer, S.L. (2005). Geotechnical Earthquake Engineering, Pearson Education, India. Kwok, K.C.S. (1984). Damping Increase in Building with Tuned Mass Damper, Journal of Engineering Mechanics, 110(11), Lee, C.L., Y.T. Chen, L.L. Chung, Y.P. Wang (2006). Optimal Design Theories and Applications of Tuned Mass Dampers, Journal of Engineering Structures, 28, Li, C. and Y. Liu (2004). Ground Motion Dominant Frequency Effect on the Design of Multiple Tuned Mass Dampers, Journal of Earthquake Engineering, 8(1), McNamara, R.J. (1977). Tuned Mass Dampers for Buildings, Journal of the Structural Division, 103(9), Ogata, K. (2005). Modern Control Engineering, Prentice-Hall of India. Ohtori, Y., R.E. Christenson, B.F. Spencer Jr. and S.J. Dyke (2004). Benchmark Control Problems for Seismically Excited Nonlinear Buildings, Journal of Engineering Mechanics, 130(4), Sadek, F., B. Mohraz, A.W. Taylor and R.M. Chung (1997). A Method of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications, Earthquake Engineering and Structural Dynamics, 26, Soong, T.T. and G.F. Dargush (1997). Passive Energy Dissipation Systems in Structural Engineering, John Wiley and Sons, New York. Wang, A.-P. and R.-F. Fung (2000), Dynamic Analysis of Tall Building with a Tuned Mass Damper Device Subjected to Earthquake Excitations, Journal of Sound and Vibration, 244(1), Warburton G.B. (1982). Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, Earthquake Engineering and Structural Dynamics, 10, Wong, K.K.F. and Y.L. Chee (2004). Energy Dissipation of Tuned Mass Dampers during Earthquake Excitations, The Structural Design of Tall and Special Buildings, 13,

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