Research Article  Open Access
Xiaoli Wu, Wei Guo, Ping Hu, Dan Bu, Xu Xie, Yao Hu, "Seismic Performance Evaluation of BuildingDamper System under NearFault Earthquake", Shock and Vibration, vol. 2020, Article ID 2763709, 21 pages, 2020. https://doi.org/10.1155/2020/2763709
Seismic Performance Evaluation of BuildingDamper System under NearFault Earthquake
Abstract
The buildingdamper system designed by a seismic code is usually considered to be able to withstand the attack of strong earthquakes. However, nearfault earthquakes, especially those with the forwarddirectivity effect, might cause early and unexpected failure of codedesigned dampers and consequent severe structural damage. In this paper, by taking into account nearfault earthquakes, seismic performance of the buildingdamper system and damper failure’s influence are evaluated systematically. A 9storey steel building is designed by the Chinese seismic code as the benchmark model, and five typical dampers, including bucklingrestrained brace damper (BRB), friction damper (FD), selfcentering damper (SCD), viscous damper (VD), and viscoelastic damper (VED), are adopted. It was found that the buildingdamper systems show a large response and possible damper failure under the nearfault earthquake excitations. Then, the influence of damper failure is investigated, which reveals that damper failure would significantly affect seismic performance of the buildingdamper system, especially for the buildingSCD system. Subsequently, by introducing the artificial nearfault earthquake excitation, the influences of different pulse parameters, such as pulse velocity amplitude, pulse period, and the number of significant pulses, are studied. It shows that the pulse velocity amplitude and pulse period obviously affect the seismic performance, while the number of significant pulses presents little influence.
1. Introduction
The strong earthquakes occurred worldwide in recent decades have led to severe structural damage of buildings. The numerical and experimental analysis of structures have been fully researched [1–5], and recent research has demonstrated that seismic response of the building can be well controlled by supplementing codedesigned dampers under farfault earthquakes [6, 7]. However, nearfault earthquakes usually possess distinct effects which are different from farfault earthquakes, such as the forwarddirectivity effect resulting in early and unexpected failure of codedesigned dampers and severe damage of the building [8–10].
Nearfault earthquakes with the forwarddirectivity effect usually exhibit immense energy concentrated on narrow period bands. This energy is observed as distinct and highvelocity pulse on velocity timehistory curves [11–13]. These characteristics have attracted a great deal of attention, making the forwarddirectivity effect an important study in the structural seismic analysis field. Vafaei and Eskandari [14] investigated the seismic performance of steel bucklingrestrained braced (BRB) frames with mega configuration under nearfault earthquakes. They further studied the influence of nearfault earthquakes on steel mega brace frames equipped with shapememory alloy braces [15]. Ghaffarzadeh et al. [16] analyzed seismic response of building frames supplemented with variable orifice dampers under nearfault earthquakes. However, the influence of the forwarddirectivity effect on seismic performance on buildingdamper systems has not been well understood because of the individual differences in each nearfault earthquake record and the scarcity of records. Moreover, the damper is usually assumed to work well without any failure under the earthquake attack.
Great effort has been made to describe the characteristics of nearfault earthquakes [17–22]; the nearfault earthquakes with the forwarddirectivity effect possess three main pulse parameters, such as pulse velocity amplitude, pulse period, and the number of significant pulses [19]. Khoshnoudian et al. [20–22] have conducted a series of studies on the soilstructure systems subjected to nearfault earthquakes. The results indicated that the structuretopulse period ratio considerably affects the high mode of the structure. In order to quantify the pulsetype effects, equivalent pulse models were adopted to artificially construct earthquake excitations [23–29]. A classical mathematical model proposed by Mavroeidis and Papageorgiou [23] could simulate nearfault earthquakes with the forwarddirectivity effect by clearly and physically interpreted and scaled input parameters. However, these proposed simplified mathematical models do not contain the highfrequency portion which is another important characteristic of nearfault earthquakes and obviously affects the seismic response of the highrise building [30, 31]. Ghahari et al. [30] further developed the method by filtering with appropriate cutoff frequency to decompose original nearfault excitations (ONE) into two components: a pulsetype excitation (PTE) possessing longperiod pulses and a background excitation (BGE) with a relatively highfrequency. An artificial nearfault excitation (ANE) can be generated by combining the BGE and the artificial equivalent pulsetype excitation (APTE) [32, 33].
The earthquake with forwarddirectivity effect generally imposes a high seismic demand on the structure, so the codedesigned damper may experience early and unexpected failure under nearfault earthquakes when adopting a seismic code which mainly considers farfault earthquakes. The damper plays an important role in resisting the earthquake attack, and experiments have demonstrated that dampers can even dissipate more than 90% of the total earthquake input energy [34]. Miyamoto et al. [35] also indicated that the failure of viscous dampers has a significant influence on the response of the structure. Therefore, it is crucial to take the damper failure into consideration when evaluating the seismic performance of the buildingdamper systems.
Dampers acting as fuses to protect the main structure of the building under earthquake excitation have been under development for years. The American Society of Civil Engineering Committee (ASCE) [36] has classified the passive dampers as five main typical dampers, including ratedependent dampers, such as viscous damper (VD) and viscoelastic damper (VED), and rateindependent dampers, such as bucklingrestrained brace damper (BRB), friction damper (FD), and selfcentering damper (SCD). In our research group, the codedesigned five typical dampers supplemented in the benchmark buildings of ASCE [37] have been utilized to analyse the progressive damage of the building subjected to the main shockaftershocks of farfault earthquakes [38]. The result shows that different dampers display different seismic performance from each other. But it did not evaluate the influence of the nearfault earthquake and considers the effect of the damper failure. The benchmark models established by ASCE [37] are commonly used as the platforms for the performance evaluation of the different control techniques [38, 39]. But the benchmark model established by ASCE is designed by the American code [40] which is different from the Chinese seismic code [41]. Thus, it is important to establish a benchmark model based on Chinese codes.
In this paper, firstly a 9storey steel building was designed by the Chinese seismic code [41] and adopted as the benchmark model. These five typical dampers were designed by the Chinese code [42]. Then, the limit values of the dampers are provided by 30 farfault earthquake records corresponding to the code design response spectra. Next, 20 nearfault earthquake records with the forwarddirectivity effect and ordinary ones are selected, and the ANEs are created by combining the BGE and APTE. Finally, the performance of the buildingdamper system under nearfault earthquakes and the damper failure’s influence are systematically investigated.
2. BuildingDamper Systems
2.1. Building Benchmark Model
A 9storey steel building adopted as the benchmark model here is designed by the Chinese seismic code [41] and PKPM software. The model configuration, component, and quality detail information are displayed in Figure 1. The material of columns is Q345 steel with the nominal yield strength of 345 MPa, while that of beams is Q235 steel with the nominal yield strength of 235 MPa. The simulation material of steel is steel01 material [43] in OpenSees, and its constitutive model object with kinematic hardening and isotropic hardening is also given in Figure 1. The finite element model was constructed in OpenSees, and all the beam and column components were modeled by the dispBeamColumn element with the fiber section [43]. The rigid floor is established by setting a master node and slave nodes so as to make uniform vibration, and the columns were fixed at base. The mass was applied and distributed proportionally to the beam nodes. In the timehistory analyses, Rayleigh damping of this building is used to obtain a damping ratio of 2% at the first period T_{1} and fifth period T_{5} [44] in order to have a suitable damping of the structure.
Table 1 compares the first three periods between the finite element model in OpenSees and the building model in PKPM, including the first period T_{1}, the second period T_{2,} and the third period T_{3}. It shows that the finite element model corresponds well to the building model in PKPM.

2.2. Five Typical Dampers
Five typical dampers, including the bucklingrestrained brace damper (BRB), the friction damper (FD), the selfcentering damper (SCD), the viscous damper (VD), and the viscoelastic damper (VED), are studied here. The dampers were installed on each storey of the 9storey building as shown in Figure 1 and modeled by the twonodelink element in OpenSees. Especially, the damper failure is a major consideration in this paper and was simulated by the “Removal” command in OpenSees in the latter chapter. The characteristics of dampers have been studied by many researchers and could be expressed by corresponding mathematical models. The hysteretic characteristics of the rateindependent dampers, such as BRB and FD, are described by the Bouc–Wen material [45, 46] as follows:where A, γ, β are the parameters that control the shape of the hysteretic loop, α is the stiffness ratio after yielding, z is a nonobservable hysteretic parameter, F_{d} is the force, u_{d} is the displacement, is the velocity, and K_{d} is the stiffness. The Maxwell material [47] is used to simulate the hysteretic characteristics of VED:where F_{c} and u_{c} are the force and displacement of the damping component and F_{k} and u_{k} are the force and displacement of the spring, respectively. The linear viscous material is utilized to represent the hysteretic characteristics of VD bywhere the parameters are identical to those of equation (1). Selfcentering material [48] in OpenSees with the constitutive model shown in Figure 2 is utilized to model the hysteretic characteristics of SCD. The parameters, such as the initial stiffness K_{1}, the postactivation stiffness K_{2,} and ratio of forward to reverse force δ, determine the hysteretic shape of SCD, where F_{0} is the forward activation force, and more detail is given in Ref. [48].
The basic design principle is as the code [42] proposed that the dampers can be seen to provide the building with the effective stiffness K_{eff} and effective damping ratio ξ_{d} which can be calculated by Equations (4) and (5):where W_{cj} is the seismic energy absorbed by the jth damper; A_{j} is the hysteretic loop area of the jth damper; W_{s} is the total energy dissipation under excitations; F_{i} is the horizontal shear force of building at ith floor; x is the horizontal displacement of dampers; F is the horizontal damping force of dampers (+ and ‒ are the positive and negative direction, respectively).
Five dampers were designed by the Chinese code [42] with the objective of reducing the maximum interstorey drift to 75% of the original value, in other words, the vibration reduction ratio is 25%. The damper design is based on the code [42], and the detail design flow can be obtained from ref. [38]. Table 2 shows the model parameters of the designed dampers, and the corresponding theoretical hysteresis curves of these five dampers are shown in Figure 3.

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2.3. Limit Values of Dampers
In this paper, the limit values of designed dampers are given by 30 farfault earthquake records corresponding to the target design response spectrum, and the frequent earthquake (FE) density of the benchmark building is of 0.2 g ground peak acceleration (PGA). These records were selected from the database of the Pacific Earthquake Engineering Center (PEER), and the general information is listed in Table 3. Figure 4 shows the acceleration spectra, and it indicated that the mean spectrum of records matches well with the target design response spectrum.

The axial displacement and force of dampers were gained by scaling these records to 0.4 g PGA which corresponds to the rare earthquake intensity in the Chinese seismic code [41]. The 1.2 times of the envelope values of corresponding displacement and force responses were assumed to be the limit values, which is given in Table 4. The limit index of each damper is selected based on the damper mechanism. The limit values of BRB, FD, and SCD are described by the displacement. The limit value of VD is related to the velocitybased damping force, and the limit value of VED is given by the maximum value of the displacement and the force.

3. NearFault Earthquake Excitations
3.1. Earthquake Records
In this section, 10 nearfault earthquake records with obvious forwarddirectivity effect and other 10 ordinary records with no obvious characteristic effects were selected from the database of the PEER center. These records belong to two famous earthquake events located at the Imperial Valley of America and ChiChi of the Taiwan region. The detailed information is listed in Table 5, and the site type refers to the NEHRP classification [49]. Figure 5 shows the velocity timehistory curves, and it indicates that the obvious difference between the forwarddirectivity and ordinary nearfault earthquakes is the distinct velocity pulse and high peak ground velocity (PGV). The velocity pulse of the forwarddirectivity nearfault earthquake can be parameterized by the velocity amplitude of pulse, the pulse period, and the number of significant pulses.

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3.2. Artificial Earthquake Excitations
The scarcity of nearfault earthquake records promotes the development of artificial earthquake excitations to facilitate the study of the influence of pulse parameters, such as velocity amplitude, the pulse period, and the number of significant pulses, on seismic response of the buildingdamper system. It is critical for the artificial pulsetype excitation (APTE) to capture the important characteristics of the natural nearfault earthquake records. Firstly, the original nearfault earthquake excitation (ONE) was decomposed into two components: the pulsetype excitation (PTE) possessing longperiod pulses and the background excitation (BGE) with a relatively highfrequency component. Next, the APTE was set up by a mathematical model to replace the PTE. Therefore, an artificial nearfault excitation (ANE) can be generated by combining the BGE and the APTE. A mathematical model with physical interpretation was proposed by Mavroeidis and Papageorgiou [23] to simulate the pulsetype excitation, which is given as follows:where A and f_{p} are the amplitude and excitation frequency, respectively; t_{0} specifies the epoch of the envelope’s peak; φ is the phase of the amplitudemodulated harmonic; and γ is the parameter that defines the oscillatory characteristics of excitation. The parameters A, f_{p,} and t_{0} are preliminarily determined according to the original excitation, while the parameters γ and φ need to be adjusted several times so that the relative error between the velocity of APTE and PTE is less than 5%.
In this section, the nearfault earthquake record TCU039 is adopted as the ONE, and the corresponding parameters of APTE are listed in Table 6. The ANE can be synthesized by combing the BGE and the APTE, which is expressed by the following equation:

Figure 6 compares the velocity timehistory curves between the ANE and ONE, and their response spectra are shown in Figure 7. It indicates that the ANE coincides well with the ONE, and it can be seen as an effective artificial excitation representing nearfault earthquake.
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4. Influence of the ForwardDirectivity Effect
Figure 8 shows maximum interstorey drifts and maximum response standard deviation of the building subjected to nearfault earthquake records. It is observed that the mean value of drift responses of the building under the forwarddirectivity effect records is obviously higher than those under the ordinary records. While the ordinary records and the forwarddirectivity records adopt the same PGA, the PGVs are distinctly different due to the velocity pulse. The highspeed velocity pulse of the forwarddirectivity record produces higher response demands and larger nonlinear deformation of the building. Moreover, the dispersion of the seismic response is larger for the forwarddirectivity records, which is evidenced by the maximum response standard deviation of the interstorey drift, that is, 0.0137 for the forwarddirectivity records and 0.0047 for the ordinary records, respectively. The lowfrequency velocity pulse in the forwarddirectivity records generally excites the vibration of loworder modes of the building, while the ordinary records lead to vibration response of the highorder modes. This conclusion was also given by Vafaei and Eskandari [14, 15].
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The TCU039 record presents obvious forwarddirectivity effect, and the CHY010 record has no obvious characteristic effects which can be considered to be the ordinary record. The two records are obtained from stations with the same site type, and the stations are in close distances of 19.89 km and 19.93 km from the fault. Thus, the significant difference between the TCU039 and the CHY010 is the forwarddirectivity effect. Figure 8(c) gives the maximum interstorey drift of the building under TCU039 and CHY010 excitations. The same conclusion is given as discussed above. It can be explained by the acceleration spectra shown in Figure 9. For TCU039 excitation, the value of the spectra acceleration of the first period of building is larger than that of the higher period, such as the second period T_{2} and the third period T_{3}, while CHY010 excitation exhibits contrasting results.
5. Seismic Performance of BuildingDamper System
5.1. Assumption of No Damper Failure
In this section, seismic analysis of the building is conducted based on the assumption of no damper failure under earthquake, and five buildingdamper systems are subjected to the forwarddirectivity nearfault earthquake and ordinary one, such as the TCU039 record and the CHY010 record. Figure 10 presents the maximum interstorey drift of the buildingdamper system under the frequent earthquake (FE), the occasional earthquake (OE), and the rare earthquakes (RE). The vibration control performance is described by the vibration reduction ratio given bywhere λ is the vibration reduction ratio, r_{0} is the maximum interstorey drift of the building, and r_{d} corresponds to the maximum drift response of the buildingdamper system. According to the response magnitude of the interstorey drift of the building, earthquake excitations are ordered as follows: the FE of CHY010, the OE of CHY010, the FE of TCU039, the RE of CHY010, the OE of TCU039, and the RE of TCU039. Figure 11 presents the curves of the vibration reduction ratio of the buildingdamper systems. It can be seen that the vibration reduction ratios of FD, VD, and VED decrease with the increase of the interstorey drift response of the building. While the vibration reduction ratios of SCD are nearly identical, the vibration reduction ratios of BRB are small at the high and low interstorey drift responses of the building but large at the moderate drift.
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Figure 11 compares the vibration reduction ratios of buildingdamper systems with five types of dampers. Ratedependent dampers, such as VD and VED, can provide stable and similar vibration reduction effects. The performances of rateindependent dampers, such as BRB, FD, and SCD, are generally related to the relative displacement response, and the plastic cumulative displacement occurs and accumulates under nearfault earthquake excitations. The FD dissipates energy through a friction mechanism between the plates, and it performs well under small excitations, while under great excitations, the performance deteriorates greatly. The BRB generates sufficient axial force while a large displacement occurs and then dissipates seismic energy. Its vibration reduction performance could not be fully utilized in the FE of CHY010 and is optimal among the five typical dampers for the OE of CHY010. The SCD can automatically reset, so no permanent displacement accumulates, and the vibration reduction ratios of SCD under different earthquake intensities are stable.
It is well known that the dampers control the vibration performance of the building through the energy dissipation. In order to further study the energy dissipation of the dampers, Figure 12 shows the dissipated energy by dampers on each floor when subjected to the OE of CHY010 and TCU039. The dissipated energy of the dampers is larger when they are under the TCU039 (with forwarddirectivity effect) than that of the CHY010 (with no obvious characteristic effects). But the energy dissipated by different dampers increases at different rates. And it can also be seen from the previous discussion that the vibration reduction ratios of SCD remain the same due to its selfreset characteristics, while other dampers are reduced. Furthermore, it is consistent that the damper dissipated more energy as shown in Figure 12 and has a higher vibration reduction ratio shown in Figure 11 when under the same earthquake records.
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5.2. Influence of Damper Failure
As discussed above, five typical dampers possess different vibration control performance under nearfault earthquake records. However, an important assumption of no damper failure is adopted in the above analysis. Actually, dampers are possible to undergo unexpected failure under strong nearfault earthquake attack. Thus, the influence of damper failure on seismic response of buildingdamper systems should be considered. In the software OpenSees, the “removal” command is used when the dampers reach the limit values. The analysis indicates that five buildingdamper systems still work under the RE of ordinary earthquakes, but would experience damper failure under most of the forwarddirectivity nearfault earthquakes in the RE intensity which are shown in Table 7. It also proves that the nearfault earthquake records with forwarddirectivity effect cause more severe damage to the building than the ordinary ones. Because of the space limitations, one typical earthquake TCU039 under which the whole five dampers have failed is selected to conduct the indepth analysis of damper failure and their influence on the buildingdamper systems.

Figure 13 presents the displacement responses of the top storey of buildingdamper systems subjected to the TCU039’s RE excitation, and the damper failure information is marked. It can be seen that five dampers of different storeys have experienced failure at different time. The seismic response of dampers excited by the TCU039 record exceeds the corresponding limit values, and the influence of pulse parameters of nearfault earthquake would be discussed in Section 6. Figure 13 also indicates that the early and unexpected damper failure has obvious effect on the seismic response of buildingdamper systems and with the accumulation of seismic energy, more and more dampers fail and the influence of damper failure increases and the displacement response of the building becomes large.
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Figure 14 gives the interstorey drift response of buildingdamper systems under the TCU039’ RE excitation. The result shows that the damper failure distinctly affects the vibration reduction performance. The vibration reduction of the SCD is most sensitive to damper failure, and it leads to more than doubled interstorey drift increase when the damper fails.
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The dampers supplemented on the building actually provide the additional stiffness and damping to reduce the seismic response. Sehhati et al. [13] discovered that the additional damping usually does not play a key role in the vibration control of buildingdamper systems under the pulsetype ground motion and additional stiffness is important. As shown in Table 2, the VD merely provides additional damping to the building and other four dampers can produce additional stiffness. The SCD adds distinct stiffness to the building, the BRB and VED followed, and the FD produces limited stiffness. When the VDs in several storeys fail in earthquake, the interstorey drift increase of the buildingdamper system is relatively small. Conversely, the maximum interstorey drift increases more than twice of the buildingSCD system if the SCD fails. It can be concluded that the influence of damper failure on seismic response of the buildingdamper system under nearfault earthquake is obvious if dampers could provide great additional stiffness. The interstorey drift of the buildingFD system decreases when the FD fails, but the influence is not obvious as the FD only provided limited stiffness.
6. Influence of Pulse Parameters
TCU039 of ChiChi earthquake is adopted here as the original nearfault earthquake excitation (ONE) with forwarddirectivity effect. As shown in Table 5, the peak ground acceleration (PGA) of the TCU039 record is 0.2 g. The artificial nearfault earthquake excitation (ANE) which could catch the main characteristics of the ONE is generated by combing the background excitation (BGE) and the artificial pulsetype excitation (APTE). The pulse parameters could be expressed by the adjustable parameters in the mathematical model of APTE. Then, the influence of pulse parameters on damper failure and seismic performance of buildingdamper systems is systematically analyzed.
6.1. Pulse Velocity Amplitude
The ANE is synthesized by setting different pulse velocity amplitudes (PVA) which is different from the peak ground velocity (PGV). The amplitude of the APTE, that is, the parameter A in the mathematical model in equation (7), varies in the range of 30∼160 cm/s. The other parameters are consistent with the ONE, as shown in Table 6. Table 8 lists the storeys where five dampers fail under ANEs with different PVAs. The BRB, FD, SCD, and VED all undergo failure when the PVAs are greater than 80 cm/s while VD does not fail and always works well. This is because the PVA mainly influenced the displacement response rather than the velocity response and the VD’s failure concerns about the velocity. Figure 15 shows seismic response of the top storey of the buildingVD system. It is seen that the displacement response increases as the PVA increases, while the velocity response value is almost the same. Therefore, for the displacementdependent damper, such as BRB, FD, SCD, and VED, more dampers of different storeys would fail as the PVA increases.

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Figure 16 gives the interstorey drift responses of buildingdamper systems under the ANEs with different PVAs of 30, 50, 80, 100, 130, 150, and 160 cm/s. It shows that the maximum interstorey drift of the buildingBRB, buildingFD, buildingSCD, and buildingVED systems increases with the increasing of PVAs. For the buildingVD system, the influence of the PVA does not give an obvious regular pattern as the VD is a ratedependent damper whose damping force is related to the interstorey velocity and the building velocity response almost maintains the small value corresponding to different PVAs. The PVAs of 50, 130, and 160 cm/s were selected as examples to compare the vibration reduction performance of five buildingdamper systems, which is shown in Figure 17. It is clearly observed that the VD had an excellent energy reduction performance at a large PVA that far exceeded other four dampers, but relatively poor performance when the PVA is small, such as at 50 cm/s. As for the other four dampers, when the PVA is small, they have nearly identical vibration control performance. With the increase of PVA, there exists a little difference of vibration reduction performance.
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6.2. Pulse Period
In this case, the PVA of APTE is extracted from the ONE, that is, 38.16 cm/s, and other parameters of ANE except for the pulse period are consistent with the ONE. The influence of pulse periods on damper failure and seismic response of buildingdamper systems are investigated, and the ratio T_{p}/T of the ANE’s period to the first period of building ranges from 0.3 to 2.0. Table 9 lists the storeys where the five dampers fail under ANEs with different pulse periods. It is found that the pulse period generally affects the damper failure. Five typical dampers in different storeys all have failed in this range of pulse periods, and the failure condition is severer when the T_{p}/T is around 1.0. Figure 18 shows the seismic response of the top storey of the buildingBRB system as an example. It shows that both displacement and velocity responses are affected by the pulse periods, and their peak values are larger as the period ratio T_{p}/T is closer to 1.0. Therefore, the damper failure is prone to happen when the buildingdamper system is subjected to ANE with T_{p}/T around 1.0. To be more precise and meticulous, the maximum value of the peak displacement response happens when the T_{p}/T is equal to 1.2, while the maximum value of the peak velocity response occurs when the T_{p}/T is equal to 1.0. This can exactly explain the phenomenon shown in Table 9 that the VD failed when the T_{p}/T is equal to 1.0, while the FD failed when T_{p}/T is equal to 1.2.

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Figure 19 gives the maximum interstorey drifts of buildingdamper systems subjected to ANEs at the period ratios from 0.3 to 2.0. The peak interstorey drifts of all five buildingdamper systems all reach their maximum values when T_{p}/T is 1.2, and the effects of the pulse periods are constant when T_{p}/T exceeds 1.2. This is because the buildingdamper systems mainly respond at the fundamental mode when T_{p}/T reaches 1.2. The fundamental mode of five buildingdamper systems in the grey line is marked in Figure 19, and it can be seen that the response shape when T_{p}/T reaches 1.2 is more similar to that of the fundamental mode. It can also be seen that when the pulsetobuilding period ratio is small, the higher mode of the buildingdamper systems is activated and accounts for larger number of components. While the pulse period elongates, the components of the higher mode decrease, and the buildingdamper systems mainly respond at the fundamental mode. This phenomenon is similar to the work of Khoshnoudian et al. [20–22].
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As for the BRB, FD, and SCD dampers, the interstorey drift when T_{p}/T equals to 0.8 is larger than that when T_{p}/T is 1.0. This can be explained by the acceleration spectra, shown in Figure 20. The acceleration spectra value of the first period of these three buildingdamper systems is large when the T_{p}/T is 0.8 then that when the T_{p}/T is 1.0.
6.3. Number of Significant Pulses
In this case, the PVA and pulse period of APTE are extracted from the ONE (TCU039 record), that is, 38.16 cm/s and 7.8 s (T_{p}/T = 3.1), respectively. Other parameters of ANE except for the number of significant pulses are consistent with the ONE, such as the peak ground acceleration (PGA) which is 0.2 g. Artificial pulsetype excitation (APTE) with different numbers of significant pulses, such as 2, 3, 4, and 5, were simulated by adjusting the parameters γ and φ in the above mathematical model, and it is shown in Figure 21. In this paper, a wave with the amplitude of not less than 50% of the PVA is seen as a significant pulse. The influence of the number of significant pulses on damper failure and seismic response of buildingdamper systems is studied. The result shows that five typical dampers remained working, and no damper failure occurred. It is identical to the results of the buildingdamper systems subjected to the ONE of 0.2 g. Figure 22 depicts the interstorey drift of the buildingdamper systems subjected to ANEs with different numbers of significant pulses. It shows that the increase in the number of significant pulses only slightly affects seismic responses of the buildingdamper systems. It can be concluded that the number of significant pulses presents little influence on the seismic response of buildingdamper systems.
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7. Conclusions
In this paper, seismic performance of buildingdamper systems subjected to nearfault excitations with forwarddirectivity effect was analyzed and damper failure’s influence was discussed. The following conclusions are obtained:(1)The nearfault earthquake with forwarddirectivity effect causes larger seismic response of the building than ordinary ones. Codedesigned dampers probably undergo unexpected failure when subjected to the forwarddirectivity nearfault earthquakes in the rare earthquake intensity. The damper failure significantly affects the vibration reduction performance, especially for SCD whose failure leads to more than doubled interstorey drift increase.(2)Pulse velocity amplitude (PVA) of the forwarddirectivity nearfault excitation greatly affects the displacement response of the buildingdamper systems; however, the velocity response remains almost the same. Therefore, the VD which is velocitydependent can work well even under high PVA and the other four dampers would fail when the PVA is higher than 80 cm/s. The peak interstorey drifts of all five buildingdamper systems all reach their maximum values when T_{p}/T is 1.2, and the effects of the pulse periods is constant when T_{p}/T exceeds 1.2. The number of significant pulses presents little influence.
Data Availability
Some or all data, models, or code generated or used during the study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors are grateful for the financial support from the National Natural Science Foundation (no. 51878674) and the Project of Yuying Plan in Central South University.
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