ANALYTICAL ESTIMATION OF THE EFFECTIVENESS OF TUNED MASS CONTROL SYSTEM USING SHAKING TABLE EXPERIMENTS

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1 4 th World Conference on Structural Control and Monitoring 4WCSCM-182 ANALYTICAL ESTIMATION OF THE EFFECTIVENESS OF TUNED MASS CONTROL SYSTEM USING SHAKING TABLE EXPERIMENTS Z. Rakicevic A. Zlatevska and D. Jurukovski Institute of Earthquake Engineering and Engineering Seismology (IZIIS), PO Box 11, 1 Skopje, R. Macedonia zoran_r@pluto.iziis.ukim.edu.mk, saska@pluto.iziis.ukim.edu.mk jurudim@pluto.iziis.ukim.edu.mk Abstract P. Nawrotzki GERB Vibration Control Systems, Berlin/Essen, Germany Peter.Nawrotzki@gerb.de Based on very large experimental data, obtained by shaking table testing of a hypothetical building with and without GERB TMCS, mathematical modeling has been done using CSI SAP2 computer program. A large number of analyses have been performed in order to model complex behavior of the TMCS. Its mechanical properties have been tuned using acceleration and displacement time histories recorded at TMCS level. Verification of analytical model has been done by comparing analytical and experimental response time histories, FFT amplitude spectra, power in band ratios and cross correlation functions and coefficients. The effectiveness of the TMCS was estimated by comparing experimentally obtained response time histories, and comparing analytical data obtained for different mass ratios and corresponding optimum tuning parameters, as well as for different location of the TMCS along the height of the structure. Compared are response time histories and power in band ratios of various kinematic quantities and internal element forces, for TMCS and fixed base model. The results showed that the TMCS has capacity for reducing of structural response by factor more than two, depending of the storey level, comparing with the fixed base case, and by installing more than one TMCS at different floor levels and with appropriate tuning of different modes improving of the structural behavior for different dynamic excitation having different frequency content, could be obtained. Introduction A five story, three bay steel frame model of a hypothetical building with total mass of approximately 19. t, having Tuned Mass Control System (TMCS) produced by GERB GmbH, Germany installed at the top, has been tested on biaxial shaking table. Large number of experimental data has been collected in terms of stresses, and time histories of displacements and accelerations at all floors have been recorded. Mathematical modeling of the tested model, with and without TMCS, has been done using CSI SAP2 computer program. The tested model is modeled as 3D frame structure using frame elements for columns, longitudinal beams, bracings and transverse beams, while the TMCS, which was installed at the top of the tested model on a steel base plate, is modeled using link elements for springs and dampers. Based on experimental data obtained from the testing analytical model and dynamic properties of the main structure have been adjusted. Mechanical properties of the TMCS, stiffness of the springs, as well as damping coefficients of the viscous dampers in three orthogonal directions have been tuned using acceleration and displacement time histories recorded at TMCS level. For verification of analytical model time history analyses have been done in linear and in nonlinear range. The analytically obtained results have been compared with experimental ones through response time histories, FFT amplitude spectra, as well as comparing power in band ratios and analyzing cross correlation functions and coefficients. In order to study the effectiveness of the TMCS, since the main frame structure has very low inherent damping, a standard procedure for optimum tuning of the mechanical properties of the TMCS have been performed. Large number of analyses have been performed both for model without and with TMCS. Analyses have be done for the structure having installed TMCS at the top having different mass coefficient (μ) and corresponding optimum tuning parameters, as well as for series of arbitrary chosen damping coefficients for TMCS' dampers. Further, for the mass ratio of.189%, which Rakicevic, Zlatevska, Jurukovski and Nawrotzki 1

2 corresponds to the tested mass of the TMCS, and with optimum tuned parameters analyses have been done moving the TMCS along the height of the structure starting from first to the fifth level. For the same earthquake inputs and excitation level time history analyses for the structure without TMCS (MRF) have been done. The effectiveness of the TMCS was estimated by comparing analytically obtained response time histories, FFT amplitude spectra, and power in band ratios of the model with installed TMCS and the one without it, as well as comparing the results obtained between models with different location of TMCS along the height of the structure. Out of large experimental and analytical results, a selected data are presented in this paper. Tested Structure The geometry of the tested steel frame model is given in Fig. 1. The columns, as well as the beams are made of steel hollow profile appropriately welded at the joints. The structure in the central span has special bracing substructure, used for modeling of the stiffness and damping needed for other test, which in this case has been disconnected from the main structural system. In the orthogonal direction the frame model has only one span on a distance of 1. m, but by adding of bracing the structural stiffness, in that direction is increased several times. The height of each floor is.7 m, while all three spans are equal 1. m each. SPRINGS & DASHPOTS TMCS LEVEL LEVEL 4 DEAD LOAD LEVEL 3 LEVEL 2 LEVEL 1 REFERENT BEAM LEVEL ACCELEROMETERS BIAXIAL SHAKING TABLE DISPLACEMENT TRANSDUCERS STRAIN GAGES Figure 1. Tested model on the shaking table with position of the TMCS and transducers The total mass of the tested structure is 19. t. The mass of the TMCS system is.3 t and the base plate, on which TMCS is attached, has.4 t. The mass of the net structure is.8 t. The total mass of 19. t has been obtained by adding of steel blocks on each floor supported on such a way that they haven t any influence in changing of the stiffness of the structure. For this model 26 channels for different transducers were used. Four channels were used for shaking table control, while for recording of the responses from the tested model, in terms of displacements, accelerations and strains, the rest 22 channels were used. Experimental Program and Results Experimental program has been designed on such a way that more useful information for structural behavior of the frame structure with and without TMCS to be collected. At first, the testing has been performed for the needs of determination of dynamic properties of both structures: frame model with Rakicevic, Zlatevska, Jurukovski and Nawrotzki 2

3 active TMCS and the same frame model with locked TMCS. For this purpose the following techniques have been used: 1. Hummer test 2. Steady-state vibration test simulated by shaking table 3. Random vibration test, also simulated by shaking table 4. Free vibration test The above methods of testing provide useful information for the first natural frequencies and corresponding damping capacity. The sensitivity of the frame behavior with and without TMCS has been studied by simulating of a set of ten different earthquakes records. Eight of them are recorded during the real earthquake motion, and two are representing artificial earthquake time histories by two famous Institutions: IEEE and USNRC, both from USA. The following earthquake time histories have been simulated with the maximum amplitudes of vibration as given in Table 1: Earthquake FSD (Full scale displacement) (cm) El Centro (Montenegro) 8.7 (California) 1. (Japan) 2.8 Mexico 22. Romania 21. Turkey 37. Izmit (Turkey) 4. IEEE (artificial) 4. USNRC (artificial). Table 1. Earthquake time histories used for shaking table simulation Having in mind that the maximum displacement of the used shaking table in horizontal direction is ±12. cm, it is obvious that the most of the selected earthquake time histories are not able to be reproduced in a full scale. The simulated different earthquakes intensity was done based on the proportional scaling of shaking table displacement capacity and earthquake full scale displacement. For identification of the natural frequency of the first model of vibration for the structural model, as well as the natural frequency of the TMCS, several methods of testing have been used. Namely, besides of steady-state vibration method, the impulse test and random vibration of -1 Hz have been simulated, also. From all these tests can be concluded that the first natural frequency of the frame structure with locked TMCS is 1.92 Hz. For unlocked TMCS it was obtained that the first natural frequency is in the range of 1.92 and 2. Hz. The natural frequency of the TMCS was measured to be in the range Hz. Estimation of the viscous damping values for the steel frame structure and for TMCS was done using free vibration technique. The frame structure has very low viscous damping, approximately.6-.8%, while the TMCS has about 1. %. The effectiveness of the TMCS has been estimated based on the difference of time responses of the tested model in terms of accelerations, displacements and strain measurements for identification of axial loads and bending moments, for both types of structural model. Rakicevic, Zlatevska, Jurukovski and Nawrotzki 3

4 Acceleration (mm/s^2) Acceleration (mm/s^2) Acceleration (mm/s^2) Acceleration (mm/s^2) Locked Unlocked EL CENTRO SPAN Locked Unlocked IEEE SPAN TURKEY SPAN 3 KOBE SPAN Displacement (mm) Displacement (mm) Displacement (mm) Displacement (mm) IEEE SPAN EL CENTRO SPAN 1 KOBE SPAN 1-1 TURKEY SPAN Figure 2. Comparison of acceleration ad displacement response time histories recorded at level for four different earthquakes Out of large number of recorded time histories for both locked and unlocked TMCS responses of comparison of time responses for accelerations and relative displacements at fifth level are presented in Fig. 2, for El Centro and earthquakes simulated with SPAN 1, as well as IEEE and Turkey Earthquakes simulated with SPAN 3. For these SPANs the PGA (in this case on the shaking table) for all these four earthquakes were simulated to be.4 g. The displacement of the TMCS (unlocked case) was recorded to be 24.2 mm, 29.mm, 32.7 mm and 27.1 mm, for El Centro, IEEE, and Turkey earthquake respectively. For locked TMCS the bending strain of the center column were recorded to be 4 to 734 με, while for unlocked case these strain has a value of 33-39με which are below yielding point. From Fig. 2 is visible that the effective control of TMCS on the structural response is different for these four selected earthquakes. Namely, in the case for El Centro and IEEE earthquakes the effectiveness of the TMCS is evident after the third second of time duration, while for the earthquake the effect of the TMCS appears after 7-th second of time duration with continuously decreasing the amplitude of motion. Visually from the Fig. 2, for Turkey earthquake it can be seen that the effectiveness of the TMCS is much larger after the 1 seconds of time duration, compared with the effectiveness of control in the first 3 seconds. The effectiveness of control for other simulated earthquakes is more or less in the same range as it is given by these four cases. 1 Rakicevic, Zlatevska, Jurukovski and Nawrotzki 4

5 Analytical Modeling Mathematical modeling of the tested model, with and without TMCS, have been done using CSI SAP2 computer program. The tested model is modeled as 3D frame structure using frame elements for columns, longitudinal beams, bracings and transverse beams, while the TMCS, which was installed at the top of the tested model on a steel base plate, is modeled using link elements for springs and dampers. Based on experimental data obtained from the testing analytical model and dynamic properties of the main structure have been adjusted. Mechanical properties of the TMCS, stiffness of the springs, as well as damping coefficients of the viscous dampers in three orthogonal directions have been tuned using acceleration and displacement time histories recorded at TMCS level and the results are given in Table 2. Spring VER Z HOR X HOR Y Damper VER Z HOR X HOR Y kn/m kns/m Table 2. Properties of the TMCS used in analysis for model verification Earthquake time histories recorded at shaking table level have been used as input for analysis in SAP2. Large number of analysis has been performed both for model without and with TMCS. The time history analyses have been done in linear and in non-linear range. The analytically obtained results have been compared with experimental ones through response time histories, FFT amplitude spectra, as well as comparing power in band and analyzing cross correlation functions and coefficients. From the experimental testing it was observed that the behavior of the TMCS is more complex than it was modeled using SAP2 program in this study. Even though, the analytically obtained results have shown a good correlation with experimentally obtained ones. The comparison of analytically obtained vs. experimentally response time histories and FFT amplitude spectra for Level acceleration and displacement of TMCS for El Centro is given in Fig. 3 Amplitude Amplitude 4 ANL 37 3 El Centro EXP Frequency (Hz) FFT Amplitude Spectrum ACC Level TMCS El Centro ANL EXP Frequency (Hz) 4 4 Acceleration [mm/s^2] Relative Displacement [mm] Level ANL -3 El Centro EXP TMCS - ANL El Centro EXP Figure 3. Comparison analytical and experimental FFT spectra and response time histories In addition, to measure the similarity of analytical and corresponding experimental response time histories the cross correlation coefficients of analytical vs. experimental results for accelerations and displacements are given in Fig. 4. The data for cross correlation coefficients for the displacements on the first storey is omitted due to incorrectness in recorded data for that level. It is evident that, having in mind the comparison of response time histories and corresponding FFT spectra, the cross correlation between analytical and experimental results is within rage of Rakicevic, Zlatevska, Jurukovski and Nawrotzki

6 Cross Correlation Coeff ACCELERATION TMCS Storey Cross Correlation Coeff REL DISPLACEMENT TMCS Storey Figure 4. Cross correlation coefficient for acceleration and displacement time histories In order to study the effectiveness of the TMCS, since the main frame structure has very low inherent damping, a standard procedure for optimum tuning of the mechanical properties of the TMCS have been performed. Large number of analyses have been performed both for model without and with TMCS. Analyses have be done for the structure having installed TMCS at the top having different mass coefficient (μ) and corresponding optimum tuning parameters, as well as for series of arbitrary chosen damping coefficients for TMCS' dampers. Further, for the mass ratio of.189%, which corresponds to the tested mass of the TMCS, and with optimum tuned parameters analyses have been done moving the TMCS along the height of the structure starting from first to the fifth level. For the same earthquake inputs and excitation level time history analyses for the structure without TMCS (MRF) have been done. Out of large number of analytical data, selected data from the time history analyses showing comparative presentation of the response time histories for acceleration at Level, and axial forces in center columns, for the TMCS model with optimum tuning parameters and fixed base model (MRF) for El Centro, IEEE and earthquakes scaled to max PGA for which response of the fixed base model is at the upper limit of linear behavior, are presented in Fig. The effectiveness of the TMCS is evident and has the same tendency as in the case of comparison of experimental results. Acceleration [mm/s^2] Acceleration [mm/s^2] Acceleration [mm/s^2] EL CENTRO PGA=.7g Level 7. EL CENTRO PGA=.7g Corner Column MRF TMCS -7. MRF TMCS Level IEEE PGA=.7g KOBE PGA=.8g Level Axial Force [kn] Axial Force [kn] Axial Force [kn] IEEE PGA=.7g KOBE PGA=.8g Corner Column Corner Column Figure. Comparison of response time histories for TMCS and FIXED model Rakicevic, Zlatevska, Jurukovski and Nawrotzki 6

7 The effect of the mass ratio (μ) of TMCS' mass and mass of the main structure has been studied through ratios of power in band of response time histories for acceleration and displacement at Level, for TMCS model and model without it, and for four different earthquake inputs, The results are presented in Fig. 6. It can be seen that as the mass of the TMCS increases the accelerations and displacements decreases, except for the earthquake for which increasing the μ above the % there is very small effect on further improvement of the displacement response. The location of the TMCS has also effect on the structural response compared to the response of the model without TMCS (MRF). In Fig. 7 are presented power in band ratios of TMCS model vs. MRF of the response time histories for acceleration and displacement at Level for different locations of the TMCS along the height of the structure. Moving the TMCS from first to fifth level the effectiveness of TMCS increases resulting in a significant reduction of the power for both accelerations and displacement response histories, starting from.6-.9, when TMCS is on the level 1, up to.1-.2 when the TMCS is located at the Level. Power in band(tmcs/mrf) ACCELERATION LEVEL REL DISPLACEMENT LEVEL.2.2 Power in band(tmcs/mrf) Figure 6. Power in band ratios for accelerations and displacements at Level Power in Band (TMCS/MRF) Acceleration Level Rel. Displacement Level Power in Band (TMCS/MRF) Location of TMCS (Level) Location of TMCS (Level) Figure 7. Power in band ratios for accelerations and displacements at Level -TMCS vs. MRF Power in Band (TMCS/TMCS) Acceleration Level Rel. Displacement Level Power in Band (TMCS/TMCS) Location of TMCS (Level) Location of TMCS (Level) Figure 8. Power in band ratios for response at Level -TMCS i vs. TMCS However, when comparing the effect of TMCS when it is located on 3-rd and then on 4-th level the difference in effectiveness of the TMCS in reducing the power in band and structural response is from 4% to 1%, compared to the effectiveness when TMCS is locate at the top on Level. This tendency is more clearly presented on Fig. 8 on which are presented ratios of power in band of the response time histories for acceleration and displacement at Level for TMCS located at different level versus TMCS located at -th level. This point to the conclusion that TMCS not necessarily should be located Rakicevic, Zlatevska, Jurukovski and Nawrotzki 7

8 at the top of the structure, since the similar effect could be obtained if the TMCS is located at lower levels. Even more, installing more than one TMCS along the height of the structure and with appropriate tuning more modes could be controlled, thus improving the structural behavior on different dynamic excitation having different frequency content. Conclusions Intensive experimental programme performed on a five story steel frame structure with and without TMCS located on the fifth floor offered a large number of valuable experimental results for development of an appropriate mathematical model. Using given geometry, the mass of the structural model and TMCS characteristics, mathematical modeling of the tested model, with and without TMCS, have been done using CSI SAP2 computer program. The tested model is modeled as 3D frame structure using frame elements for columns, longitudinal beams, bracings and transverse beams, while the TMCS, which was installed at the top of the tested model on a steel base plate, is modeled using link elements for springs and dampers. From the testing it was observed that the behavior of the TMCS is more complex than it was modeled using SAP2 program in this study. Even though, the analytically obtained results have shown a good correlation with experimentally obtained ones. Based on developed mathematical model different analyses have been performed. It has been demonstrated that by increasing of the mass ratio the effectiveness of TMCS will be increased. Further, location of TMCS has influence on the effectiveness of TMCS and as location approaches the top of the structure the effect is higher. However, analyses show that TMCS not necessarily should be located at the top of the structure, since the similar effect could be obtained if the TMCS is located at lower levels. Installing more than one TMCS at different floor levels and with appropriate tuning of different modes improving of the structural behavior for different dynamic excitation having different frequency content, could be obtained. Acknowledgements The authors of this paper are expressing thankfulness to the technical staff of Dynamic Testing Laboratory at the Institute of Earthquake Engineering and Engineering Seismology in Skopje, Republic of Macedonia, for their assistance in performing of the experimental testing. References Hartog, D. (196), Mechanical Vibrations, McGraw-Hill Jurukovski, D., and D., Mamucevski (1986), Biaxial System for Earthquake Simulations with Three-variable Control, VII European Conference on Earthquake Engineering. Lisbon Portugal September 7-12, Proceedings. Connor, J., J., (23), Introduction to Structural Control, Pearson Education, Inc. Nawrotzki, P., and N., Chouw (24), Effectiveness of Tuned-Mass Dampers in Reducing the Response of Soil-Structure Systems to Near-Source Earthquakes, The 11th International Conference on Soil Dynamics & Earthquake Engineering, Berkeley, California, USA. Jurukovski, D., and Z., Rakicevic, (24), Shaking Table Testing of the Steel Frame Model with and without GERB TMCS. IZIIS Report 24-1 (not for distribution), Skopje, Republic of Macedonia. Jurukovski D., Nawrotzki P., and Z., Rakicevic (2), Shaking Table Testing of a Steel Frame Structure with and without Tuned Mass Control System, Sixth European Conference on Structural Dynamics EURODYN 2, Paris, France, 4-7 September 2, Proceedings Rakicevic, Zlatevska, Jurukovski and Nawrotzki 8

COMPARISON BETWEEN TWO OPTIMIZATION PROCEDURES FOR DAMPER LOCATION IN STEEL FRAME STRUCTURES

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