SEISMIC EFFECTIVENESS OF PIEZOELECTRIC FRICTION FAMPERS FOR PEAK RESPONSE REDUCTION OF BUILDING STRUCTURES

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1 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No SEISMIC EFFECTIVENESS OF PIEZOELECTRIC FRICTION FAMPERS FOR PEAK RESPONSE REDUCTION OF BUILDING STRUCTURES Genda CHEN 1 and Chaoqiang CHEN 2 SUMMARY The performance of a piezoelectric friction damper (PFD) and a semi-active control algorithm was evaluated with a ¼-scale, 3-story building model that was subjected to four earthquake ground motions of various intensities. For shake table tests, the damper was installed between the first floor of the building and the shake table. Both numerical and experimental results indicated that the proposed control strategy can effectively suppress the structural vibration equally under weak and strong earthquakes. It was found that a semi-active PFD with slight saturation is beneficial to the mitigation of building responses while significant saturation tends to degrade the performance of the control strategy. Further improvement in force generation efficiency of the PFD would likely make it competitive with other representative semiactive control devices. INTRODUCTION Variable friction dampers have the advantages of low operating power requirement and guaranteed dissipation of energy by friction, and therefore do not cause instability of the structure being controlled [1-4]. The key feature of these devices is providing a controllable clamping force between two bodies that slides against each other. Most of the previous works except for the study by Kannan et al. [2] assumed that slippage always occurs in a friction damper without experimental verifications. This assumption may be invalid as can be inferred from the experimental study on friction controllable sliding isolation bearings [5]. Recently, the authors introduced the PFD concept to mitigate the seismic response of building structures [6-9]. The clamping force in a PFD is regulated by piezoelectric stack actuators, which can quickly and accurately respond to a driven command such as a voltage signal. In addition, piezoelectric actuators are effective over a wide frequency band, reliable and compact in design, as demanded in civil engineering applications [10, 11]. A semi-active control algorithm was also proposed to regulate the clamping force of a PFD. The algorithm has been numerically shown effective in reducing the peak responses of a 20-story steel building [7]. More recently, the concept has been independently implemented by Durmaz et al. [15] in a prototype friction damper which gives a significantly higher control force with the same power. 1 Associate Professor, University of Missouri-Rolla, Rolla, MO, USA. gchen@umr.edu 2 Ph.D. Student, University of Missouri-Rolla, Rolla, MO, USA.

2 In this paper, the performance of the semi-active control strategy and the previously fabricated PFD [9] was evaluated experimentally. A series of shake table tests were conducted on a ¼-scale, 3-story building model controlled with the prototype PFD. Numerical simulations were also conducted to gain more insight on the experimental results. The effectiveness, adaptability and saturation effect of the PFD were addressed. An attempt is also made to compare the performances of several semi-active control devices. EXPERIMENTAL SETUP The Building Structure The structure used in this study was a ¼-scale, 3-story building model mounted on the unidirectional MTS shake table in the Structures Laboratory of Civil, Architectural, and Environmental Engineering Department, University of Missouri Rolla. The building model is 1.22 m long, 0.61 m wide and 2.54 m tall, Fig. 1. The building has a steel moment-resisting frame structure along the earthquake excitation (longitudinal) and is a hybrid moment-resisting and X-braced structure in transverse direction. A36 ST structural tees were used to build the sections of both beams and columns. The lumped mass, mainly from the steel plates on the first, second, and top floor, was 480, 446 and 432 kg, respectively. Several swept-sine tests were conducted to identify the natural frequencies of the building model. They are 2.66, 9.46 and 18.7 Hz, respectively corresponding to the 1 st, 2 nd and 3 rd mode shapes described in Fig. 2. A series of harmonic tests were then carried out with their excitation frequencies varying around the natural frequencies of the test structure. The transfer functions of floor accelerations can therefore be constructed in different frequency ranges, from which the modal damping ratios of the structure are determined with the half-power method [12]. They are 0.56%, 0.39% and 0.32% for the 1 st, 2 nd and 3 rd modes, respectively , , st mode 2 nd mode 3 rd mode Fig. 1 Building model on shake table Fig. 2 Mode shapes The Prototype PFD Device The PFD was designed and fabricated in the Structures Laboratory by Chen et al. [9]. The prototype and its schematic representation are shown in Fig. 3. The m m m damper included four piezoelectric stack actuators to modulate its clamping force, which were manufactured by Kinetic Ceramics, Inc. (KCI) with PZT-100 material doped with Tungsten or PZWT-100. The piezoelectric constant, d 33, and the modulus of elasticity, E, of the material along the axial direction are equal to m/v and kn/m 2, respectively. Each stack is 2.54 cm in diameter and approximately 1.27 cm tall. It is composed of 24 individual piezoelectric layers stacked in series and wired in parallel, each cm thick. The damper was characterized under harmonic loading prior to shaking table tests. Its load-displacement hysteresis loops at a preload of approximately 1.78 kn are shown in Fig. 4 for an applied voltage of 0, 200, 400, 600, 800, and 1000 Volts, respectively. They are all nearly rectangular in shape. The damper was installed between a bracing support and the first floor of the 3-story frame structure as seen in Fig. 1. The damper was fixed on top of the bracing support while both ends of the frictional sliding plate inside the damper was connected to the bottom side of the first floor.

3 Friction Force (kn) V = 0, 200, 400, 600, 800, 1000 Volts Displacement (cm) Fig. 3 Prototype PFD and its schematic Fig. 4 Hysteresis loop of the prototype PFD Instrumentation and Data Acquisition Four accelerometers were attached on three floors and the shake table to measure the structural accelerations and the earthquake input. Three LVDTs were installed between the structure and a standalone rigid frame to measure the absolute displacement at each floor. The internal LVDT of the shake table was used to measure the table displacement. To measure the clamping force in each of the four stack actuators, four pancake load cells were placed inside the damper unit, one in series with each actuator. A HP 1415 Data Acquisition & Control Workstation was used for both data acquisition and structural control. Within the workstation is mainly a HP E1415A Algorithmic Closed Loop Controller. It can retrieve information from the measurement systems and store it in either a Current Value Table (CVT) or a First-In First-Out (FIFO) buffer or both. The CVT and FIFO buffer provide a communication platform from the control algorithm to an external application program. It can also output control signals to drive the four piezoelectric actuators in the PFD, and ground motion signals to the shake table actuator for vibration generation. In addition, four Piezo Drivers/Amplifiers manufactured by Kinetic Ceramics Inc. were used to amplify control signals (voltage 5V) before they were applied to the piezoelectric actuators. In this study, an amplification factor of 200 was used. PFD MODEL Piezoelectric actuators used in the PFD reveal a hysteretic behavior when they are subjected to a cyclic voltage [9]. For practical purposes, however, the relationship between the applied voltage and the clamping force on the PFD can be assumed linear in a relatively small range of voltage. Based on the linear piezoelectricity, such relationship can be mathematically represented by: 4EAd33V ( N( = N pre + (1) h in which Nt () is the clamping force applied on the damper, N pre is a constant preload, A is the cross sectional area of each stack actuator, h is the thickness of each disk of the actuators, and Vt () is the voltage applied on the stack actuators. To calibrate Eq. (1) with the PFD in the range of preload of interest, each stack actuator in the prototype damper was experimentally characterized under a preload of 89, 133 and 178 N. At each preload, tests were carried out at a voltage of 200, 400, 600, 800, and 1000 V. The total clamping force of the damper from all four actuators was plotted as a function of the applied voltage in Fig. 5. A straight line that best fits the test data from the regression analysis was also included in the figure. It can be seen from this

4 figure that the straight lines corresponding to 133 and 178 N of preload are pretty close to each other. These results indicate that the behavior of the prototype damper is nearly independent of the preload when a preload of equal to or greater than 133 N per actuator is applied. The introduction of this preload eliminates the slackness in the PFD. In addition, the data from each set of tests can be well modeled by a straight line as their correlation coefficient (R 2 ) is greater than 0.99 for the cases of 133 and 178 N in preload and greater than 0.95 for the case of 89 N in preload. The linear relation between a clamping force and the applied voltage validates the use of linear piezoelectricity. This relation is also observed in Fig. 4 under harmonic loading. Clamping Force (N) N 133 N 178 N Linear (89 N) Linear (133 N) Linear (178 N) N = 0.765V R 2 = N = 0.719V R 2 = N = 0.251V R 2 = Control Voltage (V) Fig. 5 Experimental PFD model under various preloads CONTROL STRATEGY The semi-active control strategy combining the Coulomb friction, viscous, and Reid s damper mechanisms, was considered to drive the PFD. Its performance in response reduction of single- and multistory buildings has been numerically studied in the previous investigations [6, 7]. The strategy is to suppress the vibration of a structure when the structural deformation and its derivative are increasing. Mathematically, it converts to the following relation between the clamping force, N(, the structural deformation (story drift of a building), x(, and its derivative, x& ( : N pre N( = e x( + g x& ( when when e x( e x( + g x& ( + g x& ( N > N pre pre (2) in which e and g are two positive gain factors. The first part of Eq. (2) represents the passive Coulomb damper while the second part means its active counterpart. The semi-active strategy calls for active component only when the structural responses, x( and x& (, are excessive. Its power requirements can therefore be minimized. Since a Coulomb damper with a clamping force of 356N can significantly reduce structural responses to be seen later, the preload of the PFD was set to be 89N per actuator. The corresponding experimental model as shown in Fig. 5 was employed to implement the semi-active control algorithm described by Eq. (2). Therefore, the control signal, u(, was determined as follows u( = g ( e / g x( + x& ( ) 0 N pre when when e x( + g x& ( e x( + g x& ( N > N pre pre (3)

5 Since the fundamental frequency of the test structure is 2.66Hz, the optimal gain ratio [8], e/g, was approximately estimated to be rad/sec. A value of g= 7.01 kn-sec/m was used for all tests unless otherwise specified. A closed loop control strategy was designed as illustrated in Fig. 6 to semi-actively control the ¼-scale, 3- story frame structure. In the diagram, the external earthquake excitation was applied on the structure plant through the MTS shake table. The structural responses were measured with the measurement systems (Sensors). Only the shake table and the first floor displacements were extracted to compute the first story drift and drift rate for the semi-active control algorithm in Eq. (3). The control algorithm was implemented in the HP 1415A Algorithmic Closed Loop Controller by using a C like programming language. It was executed in real-time repeatedly with each execution limited within 0.01 second due to the hardware constraints in this experimental study. The execution time could be substantially reduced if a faster chip were used to run the real-time control program. The Piezo Driver/Amplifiers amplified the control signal and the amplified voltage was then sent to the four piezoelectric actuators in the prototype damper to drive the PFD. The friction of the PFD was thus physically modified and applied on the structure plant. Earthquake Input Structure Plant Sensors Responses Output PFD Damper Piezo Driver/Amplifier HP 1415A Algorithm Closed Loop Fig. 6 Closed loop control strategy In addition to the real-time control program, an external application program was developed to run on a separate CPU by using the HP VEE visual program language. This application program was designed to initialize or stop the control process, update the input earthquake excitation, and retrieve the measured structural responses from either the CVT or FIFO buffer or both, and store the data in the hard disc of the HP Data Acquisition & Control Workstation. EARTHQUAKE INPUT AND TEST PROCEDURE Two far-field and two near-field historical records were used during the experiments: the 1940 El Centro earthquake (N-S), the 1952 Taft earthquake (S69E), the 1994 Northridge earthquake (N-S), and the 1995 Kobe earthquake (N-S). Since the shake table was limited to a maximum stroke of ±2.54cm, in order to generate sufficiently large responses of the structure, the earthquake records were compressed in time scale to make their dominant frequencies approximately equal to the fundamental frequency of the structure tested. A time scale factor 1/1.816 was used for El Centro earthquake, 1/1.17 for Taft earthquake, 1/1.354 for Northridge earthquake, and 1/1.825 for Kobe earthquake. The four acceleration time histories were converted to their respective displacement time histories in voltage due to the displacement-controlled shake table system. This was done by integrating the acceleration records twice with zero initial conditions. To eliminate the drifting of velocity and displacement functions as time increases, a Butterworth high-pass filter was used to filter out the low frequency components (<0.3Hz) of both the acceleration and velocity functions. In order to investigate the

6 adaptability of the proposed semi-active control algorithm, the time histories were modified in magnitude with four different factors. The level and type of earthquake inputs used during the shake table tests are summarized in Table 1. The first letter of the name of an earthquake and a numerical number are used to designate each test case. For example, at the first level, the four earthquake inputs are respectively denoted by E1, T1, N1 and K1. They all have a peak acceleration of 0.097g; their corresponding peak displacements (stroke) are also included in the table. At other levels, not all of the four earthquakes can be simulated with the shake table because of its stroke constraint (±2.54cm). For example, at Level 2, only three earthquake inputs (E2, N2 and K2) can be simulated. For each case, defined in Table 1, three identical tests were performed to confirm the repeatability of the test data. Table 1 Multi-level earthquake inputs El Centro Taft Northridge Kobe Peak Stroke Name Stroke Name Stroke Name Stroke Name Acceleration (cm) (cm) (cm) (cm) Level E T N K1 (0.097g) Level E N K2 (0.127g) Level E K3 (0.177g) Level 4 (0.191g) K4 *g is the gravitational acceleration A series of shake table tests were conducted in the following order: 1. to understand the behavior of the uncontrolled structure under the Level 1 earthquake inputs, 2. to measure the response of the structure controlled with the semi-active strategy and the Coulomb mechanism, u(=0, from weak to strong excitations that were described in Table 1, and 3. to investigate the saturation effect of the PFD on structural responses under the K3 excitation when the control gain factor g varies from 3.50 to kn-sec/m. RESULTS AND ANALYSIS The story drift and floor acceleration of the uncontrolled structure were recorded when subjected to the first level of earthquake inputs in Table 1. Their peak values were determined and summarized in Table 2. Numerical simulations were done for all test cases in Table 1 and their peak values were also included in Table 2. It is clearly seen from Table 2 that the simulations corresponding to the first level of excitations are in good agreement with the experimental results. The majority of these comparisons show less than 10% difference. This indicates that the structural properties identified from forced harmonic vibration tests are sufficiently accurate and the frame model used for numerical simulations is representative to the building structure. The validated model will therefore be used to simulate the responses of uncontrolled structure when subjected to a higher level of earthquake inputs described in Table 1. The simulated responses will be compared with the experimental results of the controlled structure. Table 2 also indicates that the maximum peak inter-story drift always occurs in the first story while the maximum peak floor acceleration (absolute) is achieved at the third floor. The semi-active control experiments were conducted when the structure was subjected to all earthquake inputs in Table 1. The measured and numerically simulated peak responses of the semi-actively controlled structure are presented in Table 3. It can be seen that the shake table test results agree well with those from numerical simulations. This validates the implementation of the proposed semi-active control

7 algorithm in MATLAB. Shown in Fig. 7 are the experimental and simulated response time histories of the structure when subjected the earthquake input K4. Their good agreement not only confirms that the computer model is reasonably accurate but also indirectly validates the use of numerical results of the uncontrolled structure at high-level excitations for comparison with the experimental results of the controlled structure to study the effectiveness of the proposed PFD. Table 2 Peak responses of the uncontrolled structure Story drift (cm) Floor acceleration (g) Input 1 st 2 nd 3 rd 1 st 2 nd 3 rd E1 Simulation Experiment T1 Simulation Experiment N1 Simulation Experiment K1 Simulation Experiment E2 Simulation N2 Simulation K2 Simulation E3 Simulation K3 Simulation K4 Simulation Table 3 Peak responses of semi-actively controlled structure Story drift (cm) Floor acceleration (g) Input 1 st 2 nd 3 rd 1 st 2 nd 3 rd E1 Simulation Experiment T1 Simulation Experiment N1 Simulation Experiment K1 Simulation Experiment E2 Simulation Experiment N2 Simulation Experiment K2 Simulation Experiment E3 Simulation Experiment K3 Simulation Experiment K4 Simulation Experiment

8 1st Story Drift (m) rd Floor Acceleration (g) simulated semiactive simulated semiactive Time (sec) Fig. 7 Semi-actively controlled structural responses under the K4 earthquake When no control signal is applied on the PFD, the device behaves like a Coulomb damper and passively dissipates seismic energy. The PFD without the applied voltage were also implemented during the shake table tests for all test cases in Table 1. The measured and numerically simulated peak responses of the passively controlled structure are presented in Table 4. It can be observed from the table that the experimental results are in good agreement with simulations, indicating that due considerations have been taken in the modeling of stick and sliding phases of the PFD. Table 4 Peak responses of passively controlled structure Story drift (cm) Floor acceleration (g) Input 1 st 2 nd 3 rd 1 st 2 nd 3 rd E1 Simulation Experiment T1 Simulation Experiment N1 Simulation Experiment K1 Simulation Experiment E2 Simulation Experiment N2 Simulation Experiment K2 Simulation Experiment E3 Simulation Experiment K3 Simulation Experiment K4 Simulation Experiment

9 By comparing the results in Table 2 and 3, it can be seen that the proposed semi-active control strategy substantially reduced both the inter-story drift and the absolute floor acceleration of the structure. In the test case of K4, the maximum peak story drift and floor acceleration can be mitigated by approximately 73% and 63%, respectively. To see the difference over the duration of the excitation, the story drift and acceleration time histories of the uncontrolled and controlled structures are compared in Fig. 8 for earthquake input K4. It is observed from the figure that the effect of the PFD is to mainly increase the structural damping without changing the structural stiffness. In comparison with the passively controlled structure, the semi-actively controlled structure perceives a 36% less maximum peak story drift and 28% less maximum peak floor acceleration in the case of K4. This can also be seen from the comparison of their time histories in Fig. 9. However, it is worth to mention that for lower level earthquake inputs such as K1, the differences between semi-actively and passively controlled structural responses become much smaller. This is consistent with the strategy in the proposed semi-active control algorithm. That is, the active portion of control force is activated only when the structural responses are sufficiently large. 1st Story Drift (m) 3rd Floor Acceleration (g) simulation (uncontrolled) semiactive simulation (uncontrolled) semiactive Time (sec) Fig. 8 Semi-actively controlled vs. uncontrolled structural responses under the K4 excitation 1st Story Drift (m) rd Floor Acceleration (g) coulomb semiactive coulomb semiactive Time (sec) Fig. 9 Semi-actively vs. passively controlled structural responses under the K4 excitation

10 To understand the adaptability of the PFD to external disturbances, the reductions in peak story drift and floor acceleration are plotted in Fig. 10 as a function of the intensity of the Kobe earthquake input for both semi-active and passive controls. It can be seen from the figure that the semi-active strategy further reduces the structural responses in comparison with those of the passively controlled structure. In addition, with the semi-active control, the reduction in both inter-story drift and acceleration is nearly independent of the intensity of earthquake inputs. This means that the semi-active control algorithm is adaptive to multi-level earthquake inputs in suppressing structural responses. When Coulomb damping only is employed, the PFD becomes less effective as the intensity of earthquake inputs increases. These observations agree well with the conclusions drawn from the numerical study of an SDOF structure [8] Drift Reduction due to Coulomb Damper (%) st story 2nd story 3rd stroy Acceleration Reduction due to Coulomb Damper (%) st floor 2nd floor 3rd floor Kobe Earthquake Intensity (g) Kobe Earthquake Intensity (g) Drift Reduction due to Semi-Active PFD (%) st story 2nd story 3rd story Acceleration Reduction due to Semi-Active PFD (%) st floor 2nd floor 3rd floor Kobe Earthquake Intensity (g) Kobe Earthquake Intensity (g) Fig. 10 Maximum structural response reduction vs. intensity of earthquake input The previous study from numerical simulations [7] indicated that over saturation of a PFD will significantly degrade the performance of the damper. To experimentally validate this, the gain factor g in the control algorithm was allowed to vary from 3.50 to kn-sec/m and the structure with the semiactive damper was tested again on the shake table. Fig. 11 shows the reductions in maximum story drift and floor acceleration of the structure under the earthquake input K3. Both generally increase as a larger gain factor is used except for g = 8.76 kn-sec/m. This exception is pronounced in the control of floor accelerations. To interpret the results, the time histories of the first floor acceleration and the corresponding control signal are presented in Fig. 12 when g is respectively equal to 7.01, 8.76 and kn-sec/m. It can be observed that, more saturation occurs in the PFD as the gain factor increases. The saturation makes the PFD behave more like a coulomb damper with a constant voltage. As a result, the

11 damper experiences an alternation of stick and sliding phases, which likely generates minor acceleration pulses [8]. When the damper is subjected to several cycles of saturation and non-saturation within a short time period and their induced acceleration pulses coincide with the arrival of the first peak of earthquake excitation, the floor acceleration is locally amplified for g = 8.76 kn-sec/m as observed from the test results. Note that even when g = 5.25 or 7.01 kn-sec/m, slight saturation has occurred. Drift Rreduction due to Semi-active PFD (%) st story 2nd story 3rd story Gain Factor g (kn-sec/m) Acceleration Reduction due to Semi-Active PFD (%) st floor 2nd floor 3rd floor Gain Factor g (kn-sec/m) Fig. 11 Maximum structural response reduction vs. gain factor under the K3 excitation FORCE GENERATION OF THE PFD DEVICE The above numerical and experimental study proved that the concept of a PFD is promising for earthquake hazard mitigations. However, the force generated by the prototype PFD is very small for largeor full-scale building structures. To address the scalability of a PFD in the framework of future research activities, two issues are discussed below: force capacity and its required power. As can be seen in Eq. (1), the force capacity of the prototype PFD can be increased by using stronger electromechanical coupling piezoelectric materials (higher d 33 ) and thinner piezoelectric disks (smaller h). More importantly, the force capacity can directly be scaled up by using multiple friction surfaces [9]. Indeed a prototype PFD taking into these factors (18 friction surfaces) was recently designed and fabricated with one piezoelectric actuator, and tested in an independent study for machine vibration suppression [13]. The force capacity and power requirement of the new device are presented in Table 5 in comparison with other representative semi-active devices, including a hydraulic, a magneto-rheological fluid (MR), and an electro-rheological fluid (ER) damper. It is clearly seen from the table that the PFD is more compact yet capable of generating a higher force with smaller power required. With more friction surfaces created in a PFD, it is anticipated that the proposed technology is practically feasible for largeand full-scale implementations in the future. Table 5 Performance and power requirements of semi-active dampers Damper Dimension (cm) Stroke (mm) Max. Force (N) Min. Force (N) Power (W) Piezoelectric[13] ±13 11, <0.5 Hydraulic [14] Length=19.2, ±25 8, Diameter=6.35 MR Fluid [15,16] Length=21.5, ±25 3, <10 Diameter=3.80 ER Fluid [17] Length=10.0, Diameter=8.90 ±30 6,000 0

12 1st Floor Acceleration (g) 1st Floor Acceleration (g) Control Signal (V) Control Signal (V) 1st Floor Acceleration (g) Control Signal (V) Time (sec.) (a) g = 7.01 kn-sec/m Time (sec.) (b) g = 8.76 kn-sec/m Time (sec.) (c) g = kn-sec/m Fig. 12 Time history of acceleration and control signal under the K3 excitation

13 CONCLUSIONS The semi-active control strategy proposed in the previous studies has been successfully implemented in the laboratory. Based on the shake table tests and numerical simulations on a ¼-scale, 3-story frame structure, the following conclusions can be drawn: 1. The proposed semi-active control strategy can suppress both the inter-story drift and floor acceleration of the structure up to approximately 70%, or 30% more than a Coulomb damper can. 2. The semi-active strategy is adaptable to multi-level earthquake excitations, an attribute that passive Coulomb dampers do not have. 3. Slight saturation in a PFD is beneficial to earthquake mitigation of the structure while significant saturation tends to degrade the effectiveness of the semi-active control strategy due to alternating stick and sliding phases, which is consistent with that from numerical simulations [7]. 4. The proposed technology is likely scalable for practical implementations in large- and full-scale buildings by introducing more friction surfaces and more efficient piezoelectric materials. ACKNOWLEDGMENTS Financial support to complete this study was provided by the U.S. National Science Foundation under Grant No. CMS with Drs. S.L. McCabe, and S. C. Liu as Program Directors. The results, findings, and opinions expressed in the paper are solely those of the authors and do not necessarily represent those of the sponsor. REFERENCES 1. Yang C, Lu LW. Seismic response control of cable-stayed bridges by semi-active friction damping. Proceedings of the 5th U.S. National Conference on Earthquake Engineering, Chicago, USA, 1994: Kannan S, Uras HM, Aktan HM. Active control of building seismic response by energy dissipation. Earthquake Engineering and Structure Dynamics 1995; 24(5): Hirai J, Naruse M, Abiru H. Structural control with variable friction damper for seismic response. Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, 1996: Inaudi JA. Modulated homogeneous friction: a semi-active damping strategy. Earthquake Engineering and Structure Dynamics 1997; 26: Nagarajaiah S, Feng MQ, Shinozuka M. Control of structures with friction controllable sliding isolation bearings. Soil Dynamics and Earthquake Engineering 1993; 12: Chen GD, Chen CC. Behavior of piezoelectric friction dampers under dynamic loading. Liu SC, Editor. Smart structures and highways: smart systems for bridges, structures, and highways, 2000: Chen GD, Chen CC. Semi-active control of the 20-story benchmark building with piezoelectric friction dampers. ASCE Journal of Engineering Mechanics 2004; 130 (in prin. 8. Chen GD, Chen CC. Building hazard mitigation with piezoelectric friction dampers. Proceedings of the International Conference on Advances in Building Technology, Hong Kong, China 2002; 1: Chen GD, Garrett GT, Chen CC, Cheng FY. Piezoelectric friction dampers for earthquake mitigation of buildings: design, fabrication, and characterization. International Journal of Structural Engineering and Mechanics 2004; 17 (in prin. 10. Housner GW, Soong TT, Masri SF. Second generation of active structural control in civil engineering. Proceedings of 1st World Conference on Structural Control, Los Angeles, California, 1994; 1: Panel 3-18.

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