Application of an SMA-based hybrid control device to 20-story nonlinear benchmark building

Osman E. Ozbuluta and Stefan Hurlebausa,1,2

aZachry Department of Civil Engineering, Texas A&M University, College Station, TX

SUMMARY

This paper investigates the seismic response control of 20-story nonlinear benchmark building with a new re-centering variable friction device (RVFD). The RVFD combines energy dissipation capabilities of a variable friction damper (VFD) with re-centering ability of shape memory alloy wires. The VFD that is the first subcomponent of the hybrid device consists of a friction generation unit and piezoelectric actuators. The clamping force of the VFD can be adjusted according to the current level of ground motion by adjusting the voltage level of piezoelectric actuators. Shape memory alloy (SMA) wires that exhibit a unique hysteretic behavior and full shape recovery after experiencing large strains is the second subcomponent of the hybrid device. Numerical simulations of seismically excited 20-story benchmark building are conducted to evaluate the performance of the hybrid device. A continuous hysteretic model is used to capture frictional behavior of the VFD while a neuro-fuzzy model is employed to describe highly nonlinear behavior of the SMA components of the hybrid device. A fuzzy logic controller is developed to adjust voltage level of VFDs for favorable performance in a RVFD hybrid application. Results show that the RVFD modulated with a fuzzy logic control strategy can effectively reduce interstory drifts and permanent deformations without increasing acceleration response of the benchmark building for most cases. KEY WORDS: superelasticity; damper; friction device; shape memory alloy; earthquake; re-centering

1. INTRODUCTION

Protection of civil structures against natural hazards such as earthquakes and strong winds constitutes a significant task for structural engineers. Over past two decades, numerous control devices and strategies have been proposed to improve the safety and performance of civil engineering structures. Structural control systems are typically classified into three categories: passive, active and semi-active systems. Passive control systems which include base isolation systems, tuned mass dampers, and energy dissipation systems such as friction devices, metallic yield devices, and viscous fluid dampers require no external energy and have simple mechanism but they are not adaptable and effective only for a limited range of external excitations [1]. Active control systems possess attractive features such as large force capacity and adaptability [2]. However, their stability problems, reliability and large power consumptions are still major concerns to engineers. Semi-active control systems adjust physical properties of smart material and mechanical systems to control the behavior of passive devices. Since the actuators used in semi-active devices do not directly generate a control force, but instead modify the physical

1 Correspondence to: Stefan Hurlebaus, Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas, U.S.A. 2 E-mail: shurlebaus@tamu.edu

parameters of passive systems, they have small power requirements and do not cause any stability problem. The semi-active systems offer the reliability of passive devices and adaptability of active devices [3-6].

Shape memory alloys (SMAs) are novel materials that exhibit several unique characteristics [7]. Superelasticity which refers to the ability to undergo large nonlinear elastic (reversible) deformation is one of the unique properties of the SMAs. Superelastic SMAs can recover their original shape upon the removal of the mechanical load due to solid-to-solid phase transformations. Besides its excellent self-centering capability, a considerable amount of energy dissipation is possible since the behavior of superelastic SMAs is nonlinear and hysteretic. Therefore, SMAs have been considered in a wide range of applications in civil engineering. The SMA-based dampers [8-10], SMA bracing system [11-14], SMA beam-column connectors [15,16], SMA-based isolation systems [17-20], SMA bridge restrainers [21,22], and SMA column reinforcement [23,24] are among the applications to benefit from the unique combination of properties offered by SMAs.

This paper explores the performance of a novel re-centering variable friction device (RVFD) for control of the 20-story nonlinear benchmark control structure subjected to various levels of earthquakes. The RVFD has two subcomponents: superelastic SMA wires that exhibit excellent re-centering characteristics but have limited energy dissipation capability and a variable friction damper (VFD) that can be intelligently controlled to enable desired level of energy dissipation through friction. In what follows, the hybrid device and its modeling technique are described first. Then, a heuristic fuzzy controller that is employed to modulate the normal contact force of the RVFD is introduced. Next, a numerical study is performed to investigate the effectiveness of the proposed device in suppressing the response of a seismically excited 20-story nonlinear benchmark structure.

2. RE-CENTERING VARIABLE FRICTION DEVICE

2.1 Description of the hybrid device

Figure 1 illustrates experimental stress-strain curves for superelastic NiTi wires at room temperature for various loading frequencies and for various temperatures at 1 Hz. Also, the variation of the equivalent viscous damping with the loading frequency and temperature is shown in the figure. Here, the equivalent viscous damping is computed as dissipated energy per cycle (the area inside the hysteresis loop) divided by the product of 4π and the strain energy for a complete cycle [25]. It can be seen that the quantity of equivalent viscous damping provided by superelastic SMA wires is not sufficient to render the use of SMAs as the sole damping device. Also, the energy dissipation capacity of the SMAs decreases with the increasing loading rate or temperature, but the maximum resistive force of the SMA wires increases due to the increase in the loading plateau at higher loading rates and temperatures. Since an SMA-based seismic control device implemented into a structure will be subjected to dynamic loading, energy dissipation provided by the device will be fairly small. In the design of the hybrid device, this drawback is eliminated through the incorporation of a friction damper into the RVFD. Friction dampers can dissipate significant amount of energy when an optimal contact force is provided. If the contact force is very low or very high, the amount of dissipated energy will not be ample. For example, a small contact force will provide very little resistive force during a strong earthquake, while a large contact force will cause the friction device to act simply as a typical

brace rather than a damping element during a weak or moderate event. Therefore, here, a variable friction damper is employed in the hybrid device to ensure desirable level of energy dissipation.

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Figure 1. Stress-strain curves of superelastic SMAs and variation of equivalent viscous damping ratio with loading frequency and temperature

The RVFD considered in this study consists of three parts: (i) a friction generation unit, (ii) a

piezoelectric actuator, and (iii) shape memory alloy wires. Figure 2 shows a schematic diagram and a 3D rendering of the proposed RVFD. In this design of the hybrid device, the friction unit simply consists of two steel plates rubbing against a friction pad material and clamped together with high strength bolts and a piezoelectric actuator. Since piezoelectric materials cannot endure large strains that can be induced in the hybrid device during a seismic event, piezoelectric actuators are oriented perpendicular to the sliding surface of a RVFD. Four piezoelectric actuators are used in the device. The clamping force of a RVFD can be adjusted according to the current level of ground motion by adjusting the voltage level of the piezoelectric actuators. The energy dissipation capacity of the hybrid device is a function of the friction material chosen and the contact force. For a given structural system subjected to seismic loading, the desired level of energy dissipation can be obtained by a proper selection of the coefficient of friction between two bodies and varying the contact force of the device.

Superelastic shape memory alloys are employed in the hybrid device to realize re-centering ability for the device. A total of five studs are inserted into plates as shown in Figure 2. Studs 1 and 3 are inserted into the inner steel plate and mutually move with this plate. In order to enable the movement of stud 3, the outer plate has a longitudinal slot in the middle of its top and bottom surfaces. Stud 4 is similarly inserted into the outer plate, while two short studs (2 and 5) are attached to the edges of the outer plate. SMA wires are wrapped around the studs connected to the inner and outer plates. They are held in place by a screw/nut fastener. The arrangement of the wires and studs is such that either the wires in the middle group or the outer SMA wire groups are subjected to the tension. By setting the number of SMA wires in the middle group to twice as many as in the outer group, the hybrid device will exhibit symmetrical response.

SMA wires

Piezoelectric actuator

Friction interface

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A

A

Section A-A

Figure 2. Schematic illustration and 3D rendering of RVFD

2.2 Modeling of the hybrid device

A number of researchers have developed a material model to capture highly nonlinear behavior of superelastic SMAs. Since the SMAs would be exposed to dynamic loading in seismic application, it is important to consider the effects of loading rate and temperature on the mechanical response of SMAs. In this study, a rate- and temperature- dependent model developed by Ozbulut and Hurlebaus [26] is used to characterize the superelastic response of NiTi shape memory alloys employed in the hybrid device.

Adaptive neuro-fuzzy inference system (ANFIS) is an innovative approach that combines fuzzy theory and neural networks to build computationally intelligent systems for complex real world problems. In particular, the ANFIS exploits the adaptive capabilities of neural network strategies to develop a fuzzy model whose parameters (membership functions and rules) cannot be predetermined by user’s knowledge. One of the main advantages of the ANFIS is that it does not require a complex mathematical model to compute the system output. The ANFIS uses a hybrid algorithm to learn from the sample data from the system and can adapt parameters inside its network. Here, the ANFIS is used to create a model of superelastic SMAs considering

temperature and loading rate effects. First, an initial fuzzy inference system (FIS) is created which employs strain, strain rate and temperature as input variables and predicts the stress as a single output. Next, data collected from experimental tests of NiTi wires that is performed at various loading rates and temperatures is concatenated in order to set up training, checking and validation data sets for the ANFIS simulations. After training, the developed FIS is validated using the data set which is reserved for validation and not used during the ANFIS training. Figure 3 illustrates stress-strain curves of superelastic SMAs at different loading conditions for experimental tests and fuzzy model prediction. It can be seen that the fuzzy model is capable of successfully simulating the response of SMAs at each condition. Details in regard to the neuro-fuzzy model of the NiTi wires can be found in Ozbulut and Hurlebaus [26].

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Figure 3. Fuzzy model prediction and experimental hysteresis loops

The frictional force of the RVFD is decribed by a continuous hysteretic model proposed by

Constantinou et al. [27] and given as follows , )( ZtNFf µ= (1)

where µ represents the coefficient of friction; N is the contact force; and Z is a hysteretic dimensionless quantity expressed as

1 0 ,n nyu Z u Z Z u Z Auγ β

−+ + − =& & & & (2)

where uy is the yield displacement; u! is the slip velocity of the damper; and γ, β, A and n are dimensionless parameters that control the shape of the hysteresis loop. The recommended values of these parameters to provide typical Coulomb friction behaviour are uy = 0.5mm, γ = 0.5, β = 0.5, A = 1 and n=2. Note that the hysteretic quantity Z is bounded by 1± and accounts for occurrence of the stick phase of the damper [28]. Figure 4 shows the force-deformation curves of the SMA wires and friction device as well as the combined hysteresis of the RVFD.

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Figure 4. Force-deformation curves of the RVFD and its sub-components

3. NONLINEAR BENCHMARK STRUCTURE

In this study, the SAC Los Angeles 20-story structure, designed for the SAC Phase II Steel Project is selected for numerical investigations. This structure has been used as a benchmark building for nonlinear seismic control design. The benchmark structure is 30.48 m by 36.58 m in plan, and 80.77 m in elevation. The lateral load resisting system of the building consists of two steel perimeter moment resisting frames (MRFs) with gravity frame in between. The total seismic mass of the structure above the ground level is 1.11×107 kg. The first three natural frequencies of the 20-story benchmark building are 0.26, 0.75, and 1.30 Hz. The seismic response of the building is computed using a nonlinear analysis tool implemented in Matlab/SIMULINK [29]. In the evaluation model, plane frame elements are employed to model the beams and columns of the structure and a bilinear hysteresis model is used to represent plastic hinges which are assumed to occur at the moment resisting column-beam and column-column connections. The damping matrix is determined based on Rayleigh damping formulation in which 2% damping ratio is used for the first and fifth mode. A detailed description and mathematical modeling of the benchmark building can be found in Ohtori et al. [30].

The ground motions used to evaluate the performance of the RVFDs includes two far-field earthquakes (El Centro and Hachinohe) and two near-field earthquakes (Northridge and Kobe). The peak absolute accelerations of the ground motion records are 0.35, 0.23, 0.84, 0.83 g, respectively. In the benchmark study, various levels of each of the earthquake records are utilized including: 0.5, 1.0 and 1.5 times the magnitude of El Centro (Cases 1-3) and Hachinohe (Cases 4-6); and 0.5 and 1.0 times Northridge (Cases 7-8) and Kobe (Cases 9-10).

A preload of 15 kN is set on each device, corresponding to a force equal to 10% of the total frictional force of the RVFD. In order to choose design parameters of SMA wires, a trial and error procedure is usually undertaken. NiTi SMA wires cannot fully regain their original shape if they are strained over 6-7%. Here, it is aimed to keep the maximum strain of SMA wires during strongest motion within the recoverable superelastic strain range of the material. Also, the cross-sectional area of SMA wires is selected in such a way that the maximum force generated by the SMA component of the device is almost the same with that of frictional unit. All these design considerations result in the cross-sectional area and the length of the SMA wires in each RVFD to be 194 mm2 and 1.1 m. The RVFDs are installed at each story level using a chevron brace configuration.

4. FUZZY LOGIC CONTROLLER

The control strategy used to adjust the normal force of a variable friction damper highly influences the performance of the damper. A number of control algorithms and strategies including modulated homogenous friction strategy, viscous and Reid friction control strategy, and predictive control algorithm have been proposed to modulate the normal force of variable friction dampers [31-33]. In this study, fuzzy logic approach that is an effective method to deal with complex nonlinear systems is employed to develop a semi-active controller for the RVFD. Fuzzy logic controller (FLC) employs a set of simple linguistic rules to describe the relationships between inputs and outputs of a controller instead of complicated mathematical terms. The block diagram of the FLC designed to the nonlinear benchmark structure is shown in Figure 5. There are four main steps in the design of a FLC. First step is fuzzification, where the crisp numeric values of input and output variables are transformed to fuzzy variables by defining membership functions to each input. Then, a rule base is defined to relate the inputs to output by means of if-then rules. Next, an inference engine that evaluates the rules to produce the system output is employed. Finally, the output of the controller that is a fuzzy quantity is transformed to a non-fuzzy discrete value during a procedure named as defuzzification.

Fuzzification

Benchmark Building

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Figure 5. Block diagram of benchmark structure controlled by a FLC

A simple heuristic fuzzy controller is developed to adjust the contact force of the RVFD.

Acceleration measurements of 1st, 4th, 8th, 12th, 16th and 20th floors are used for feedback in the control system. Six sensors are used to measure absolute accelerations at these story levels. The fuzzy controller employs two acceleration measurements as input variables and outputs the command voltage for the RVFD. The control devices located at 1st floor up to the 4th floor use

the acceleration measurements of the 1st and 4th floors; devices at 5th floor up to the 8th floor use the acceleration measurements of the 4th and 8th floors; devices at 9th floor up to the 12th floor use the acceleration measurements of the 8th and 12th floors; devices at 13th floor up to the 16th floor use the acceleration measurements of the 12th and 16th floors; and devices at 17th floor up to the 20th floor use the acceleration measurements of the 16th and 20th floors .

Seven membership functions are defined for each input variable of the fuzzy controller and four triangular membership functions are defined to cover the domain of the output variable voltage that varies from 0 V to 10 V as shown in Figure 6. The fuzzy sets for input variables are; NL = negative large, NM = negative medium, NS = negative small, ZR = zero, PS = positive small, PM = positive medium, and PL = positive large; and for output variables are ZE = zero, S = small, M = medium, and L = large. After the fuzzification of input and output variables, a fuzzy rule base is defined for the fuzzy controller. The rule base adopted for the developed fuzzy controller is given in Table 1. The control rules are in the form of if-then rules and maps the link between the input and output membership functions. A rule in the table below can be read as “if the ith floor acceleration is negative large and nth floor acceleration is negative large, then voltage is large”. Note that a voltage amplifier is used to realize a driving voltage up to 1000 V for the piezoelectric actuators of the RVFD.

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Table 1. Fuzzy rule base of the fuzzy controller

First input Second input NL NM NS ZR PS PM PL

NL L L M M L M M NM L M S S M M S NS M S S ZR M S S ZR M S S ZR S S M PS S S M ZR S S M PM S M M S S M L PL M M L M M L L

5. NONLINEAR TIME HISTORY ANALYSES

In this section, nonlinear time history analyses of the 20-story benchmark building are conducted to evaluate efficacy of the RVFD in mitigating the seismic response of structures. A total of 12 evaluation criteria that are defined in the benchmark control problem statement [30] are computed for the benchmark structure subjected to various levels of earthquakes. The evaluation criteria J1-J3 evaluate the peak response while J4-J6 is based on normed building response, where the norm, . , is computed using the following equation

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and tf sufficiently large time to allow the response of the structure to attenuate. The evaluation criteria J7-J10 assess the building damage. These evaluation criteria are normalized with respect to the uncontrolled case and briefly explained in Table 2. J11 computes the maximum force generated by the control device and is normalized by the seismic weight of the building. J12 is the maximum displacement of the control device normalized by the peak uncontrolled story displacement. Also, two additional criteria P1 and P2, proposed originally by Yoshida and Dyke [34], are evaluated. These evaluation criteria are measures of maximum and total permanent drift ratio and computed as

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∑

(4)

where dpi = permanent interstory drift of the ith floor; hi = height of the ith floor; maxpδ = the

maximum permanent interstory drift ratio of the uncontrolled structure; and sumpδ = total

permanent uncontrolled interstory drift ratio. In order to decide on the number of device to place on each floor level, first, a uniform

distribution of the RVFDs at each floor is assumed. Then, the performance indices discussed above are computed for different cases. After a trial and error procedure, the number of control devices placed on each floor level of the benchmark structure is decided to be 7. Table 2 presents performance evaluation criteria J1-J12 for the 20-story benchmark building with RVFDs under the 10 ground motion records specified in the control problem.

It can be seen that the peak interstory drift ratio J1 is reduced for all earthquake cases by up to 55%. The results also show that the peak story acceleration J2 is decreased by up to 43% for nine records while the response is increased by 7% for one record. For the peak base shear J3, there is an increase between 4-21% for six records, while the peak base shear response is reduced up to 28% for four cases. Also, note that there is a significant reduction in the norm values of the building response (J4-J6) for most of the excitation cases.

In terms of building damage criteria, the installed RVFDs produce a reduction in the ductility index J7 by up to 63% and in the norm ductility J10 by up to 72% for all cases. The performance index J8 which evaluates the dissipated energy due to the plastic rotation at the ends of members and the performance index J9 which is the ratio of the plastic hinges sustained by the structure while controlled and uncontrolled are also significantly decreased in all cases. In terms of

control device, the control force and device stroke requirements of the RVFD appear to be acceptable. It can be seen that peak permanent drift P1 and total permanent drift P2 are mitigated by the RVFDs for all earthquake cases. In particular, the considerable residual deformations observed in the uncontrolled structure subjected to 1.5 × El Centro and 1.0 ×Kobe earthquakes are reduced by up to 96% for the El Centro earthquake and up to 88% for the Kobe earthquake. The maximum permanent deformation in the controlled structure under 1.5 ×Hachinohe earthquake remained below 2 mm. The largest residual deformation in the controlled structure is observed under the full scale Northridge earthquake. However, the total permanent deformation is still reduced by up to 36% as compared to the uncontrolled structure. Also, note that further reductions in permanent drift can be achieved by increasing the number of SMA wires in the hybrid device depending on the desired performance level.

Table 2. Performance evaluation criteria for 20-story benchmark building

Evaluation Criteria El Centro (0.5/1.0/1.5)

Hachinohe (0.5/1.0/1.5)

Northridge (0.5/1.0)

Kobe (0.5/1.0)

Maximum value

J1 Peak drift ratio 0.6417 0.7591 0.6877 0.4514 0.8744 0.6793 0.8285 0.8744 0.7025 0.6926 0.8694

J2 Peak level acceleration 0.7896 0.9991 0.7503 0.5694 1.0685 0.5908 0.8648 1.0685 0.9569 0.6340 0.9017

J3 Peak base shear 0.9570 1.1821 0.9560 0.7208 1.2049 0.8993 1.1250 1.0701 1.2049 1.0434 1.1400

J4 Norm drift ratio 0.4807 0.8640 0.5119 0.2810 0.9914 0.5335 0.9644 0.8944 0.2457 0.5518 0.9914

J5 Norm level acceleration 0.4182 0.6071 0.3973 0.3133 0.6071 0.3662 0.5970 0.5279 0.5335 0.3709 0.5975

J6 Norm base shear 0.7270 1.1322 0.6190 0.4141 1.1322 0.7043 1.1073 0.8086 0.6512 0.6951 1.0811

J7 Ductility 0.7430 0.9041 0.6227 0.3687 0.9589 0.7572 0.9589 0.9036 0.6880 0.7113 0.8863

J8 Dissipated energy - - 0.0021 0 0.4877 - - 0.3932 0.1160 0.0082 0.4877

J9 Plastic connection - - 0.0625 0 0.7500 - - 0.7500 0.6310 0.3023 0.4419

J10 Norm ductility 0.5337 0.8895 0.4236 0.2869 1.0037 0.5916 0.9675 0.9764 0.2777 0.5405 1.0037

J11 Control force 0.0117 0.0121 0.0154 0.0149 0.0190 0.0145 0.0150 0.0190 0.0173 0.0153 0.0154

J12 Device stroke 0.1667 0.1183 0.2622 0.4344 0.4344 0.2747 0.1969 0.3004 0.3176 0.3571 0.2694 P1 Peak permanent drift - - 0 0 0.9022 - - 0.9022 0.2207 0.0369 0.6372 P2 Total permanent drift - - 0 0 0.6390 - - 0.6390 0.1868 0.0481 0.4049

Time histories of the interstory drift and absolute acceleration for the top floor of the uncontrolled and controlled structures subjected to 1.5 × El Centro and 1.0 ×Kobe earthquakes are shown in Figure 7 and 8, respectively. These figures also include the force-deformation curves of the subcomponents of the hybrid device and combined hysteresis for the total RVFDs installed into the top floor. It is observed that the RVFDs can effectively damp out the building vibrations in very short duration. Besides the large decrease in displacement response, a modest reduction in the acceleration response is noted. As can be seen from the force-deformation curves, the energy is dissipated mainly by frictional component of the hybrid device. Profiles of the peak interstory drift, residual displacement and absolute acceleration for the uncontrolled and controlled structure subjected to 1.5 × El Centro and 1.0 ×Kobe earthquakes are shown in Figure 9 and 10, respectively. It should be noted that peak interstory drift and acceleration attains smaller values for the controlled structure for most of the floors. Furthermore, the permanent deformations observed almost at each floor in the uncontrolled structure especially under Kobe earthquake are significantly reduced by the installed RVFDs. Note that even though the peak interstory drifts at some floor levels such as at 1st and 2nd floors are almost the same for the uncontrolled and controlled structures under Kobe earthquake, there are large reductions in the residual deformations for the controlled structure.

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Finally, an additional set of simulations are conducted to assess the effect of temperature change on the performance of the installed RVFD. Figure 11 illustrates the evaluation criteria J1-J3 computed at ambient temperatures of 0°C, 20°C and 40°C for the controlled structure subjected to 10 different excitation cases. It can be seen that an increase in temperature slightly increases peak interstory drift J1 for most cases. The effect of temperature change on the peak story acceleration is more random. In particular, a reduction in peak acceleration is observed for

some earthquake cases as temperature differs ± 20°C from the reference temperature of 20°C, while peak acceleration slightly increases for some other cases. As temperature increases, it is noted that peak base shear J3 experience an increase for most of the excitation cases. This is due to the fact that the maximum force developed in the SMA device increases at higher temperatures. This can be also clearly seen from Figure 1 which shows experimental hysteresis loops of SMAs at different temperatures. However, note that the maximum change in the evaluation criteria J1, J2, and J3 are 9%, 14% and 11%, respectively for a ± 20°C variation in environmental temperature compared to the reference temperature of 20°C.

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Figure 11. Evaluation criteria J1-J3 computed at 0°C, 20°C and 40°C for the controlled structure subjected

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6. CONCLUSIONS

This study explores the effectiveness of a re-centering variable friction device for protection of seismically excited 20-story nonlinear benchmark building. The RVFD combines a variable friction device and shape memory alloy wires. In the hybrid device, the SMA wires are used to

achieve re-centering ability while its energy dissipation capacity is improved through friction. In particular, the normal force of the friction device is adjusted using piezoelectric actuators driven by a controllable voltage to provide desirable level of energy dissipation. Further, a fuzzy controller is developed to determine the voltage to send to the piezoelectric actuators. Nonlinear time-history analyses of the benchmark building with installed hybrid device are conducted under various levels of earthquakes. Results show that the RVFD is capable of effectively mitigating peak displacement response of the structure, while providing some level of amelioration in the acceleration response for all most all cases. Permanent deformations at each floor level are also reduced considerably. It is also shown that a temperature variation in the range of 0 - 40°C does not significantly affect the performance of the RVFDs.

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