Performance of a passive rate‐independent damping device in a seismically isolated multistory building
2022; Wiley; Volume: 29; Issue: 6 Linguagem: Inglês
10.1002/stc.2941
ISSN1545-2263
Autores Tópico(s)Hydraulic and Pneumatic Systems
ResumoStructural Control and Health MonitoringVolume 29, Issue 6 e2941 RESEARCH ARTICLEOpen Access Performance of a passive rate-independent damping device in a seismically isolated multistory building Wei Liu, Wei Liu orcid.org/0000-0003-4151-7738 School of Engineering, Tohoku University, Sendai, JapanSearch for more papers by this authorKohju Ikago, Corresponding Author Kohju Ikago ikago@irides.tohoku.ac.jp orcid.org/0000-0003-0350-0142 International Research Institute of Disaster Science, Tohoku University, Sendai, Japan Correspondence Kohju Ikago, International Research Institute of Disaster Science, Tohoku University, Sendai 980-0845, Japan. Email: ikago@irides.tohoku.ac.jpSearch for more papers by this author Wei Liu, Wei Liu orcid.org/0000-0003-4151-7738 School of Engineering, Tohoku University, Sendai, JapanSearch for more papers by this authorKohju Ikago, Corresponding Author Kohju Ikago ikago@irides.tohoku.ac.jp orcid.org/0000-0003-0350-0142 International Research Institute of Disaster Science, Tohoku University, Sendai, Japan Correspondence Kohju Ikago, International Research Institute of Disaster Science, Tohoku University, Sendai 980-0845, Japan. Email: ikago@irides.tohoku.ac.jpSearch for more papers by this author First published: 10 February 2022 https://doi.org/10.1002/stc.2941 Funding information: China Scholarships Council, Grant/Award Number: 202008050036; Grant-in-Aid for Scientific Research (B), Grant/Award Number: 21H01483 AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Summary In the 2011 Great East Japan Earthquake, low-frequency components of ground motion brought long-duration shaking to high-rise buildings in mega-cities far from the epicenter, resulting in damage to their interior and exterior walls, and unsafe conditions for the building occupants. Rate-independent linear damping (RILD) has been suggested as a viable option for simultaneously reducing the excessive displacement and floor response acceleration of a low-frequency structure. While the majority of previous studies on RILD have mainly focused on theoretical and mathematical approaches, the practical applications of RILD have not been extensively investigated. In this regard, this study aims to experimentally and analytically investigate the physical implementation of RILD for the protection of a multistory low-frequency structure. The effectiveness of the proposed passive causal RILD device, comprising a Maxwell-type damper and negative stiffness, incorporated into a seismically isolated building was investigated based on real-time hybrid simulation. Under strong ground motions, the passive causal RILD device could greatly reduce the floor response accelerations in the seismically isolated structure, compared with a linear viscous damping device. 1 INTRODUCTION With the increasing number of seismically isolated high-rise buildings, the possible excessive displacement in low-frequency structures induced by low-frequency components in an extreme seismic event has attracted considerable attention. Conventional control devices, such as fluid and hysteretic dampers, are used in reducing the displacement and floor response acceleration; however, this results in a trade-off relationship, in which the increase in the number of conventional dampers can reduce excessive displacement while compromising the floor response acceleration.1-3 Rate-independent linear damping (RILD) is an ideal linear model for simultaneously reducing excessive displacement and floor response accelerations in low-frequency structures. Particularly, this model obtains the direct displacement control through a resistive force that is proportional to the response displacement and in phase with the velocity.4-6 The behavior of RILD incorporated into structures has been extensively investigated.7-11 Crandall12, 13 identified RILD as a noncausal element, thereby hindering its physical implementation. Nevertheless, several researchers have investigated the causal approximation of RILD. Biot14 proposed the first successful causal model of RILD, which consisted of an infinite number of Maxwell elements. However, Caughey15 reported that Biot's model can only be regarded as rate-independent at high frequencies. Inaudi and Kelly16 proposed a time domain analysis method based on convergent calculations with the repeated use of the Hilbert transform. Inaudi and Makris17 proposed a method to convert the integro-differential equation of a system with RILD to a differential equation using analytic signal. Makris18 proposed the addition of an adjustable real term to the complex-valued stiffness of an ideal RILD model to satisfy the causality requirement. Makris and Zhang19 developed two causal models to estimate the nearly frequency-independent cyclic behavior of soils, thereby demonstrating causal hysteretic model as the mathematical connection between the RILD (the noncausal constant hysteretic model) and Biot's model.14 Owing to the difficulty in realizing RILD as a physical device, majority of studies on RILD have been theoretical. Thus, several researchers have focused on mathematical approaches for the causal approximation of RILD.20-29 Furthermore, there have been attempts to mimic RILD using fractional-order models.30-34 Keivan et al.35, 36 proposed a first-order all-pass filter to causally approximate RILD. Their proposed digital filter is useful for controlling a magnetorheological damper. To ensure the reliability of a device even in the case of power loss caused by a severe earthquake, Luo et al.3 used a Maxwell element in parallel with a negative stiffness unit to physically reproduce the first-order all-pass filter proposed by Keivan et al.35 Because the mass matrix derived in their study was singular, some explicit integral schemes could not be used in their numerical analysis. Liu and Ikago37, 38 developed a method to overcome the singularity of the mass matrix experienced by Luo et al.3 and performed real-time hybrid simulation (RTHS) to investigate the feasibility of a passive causal RILD device. Liu and Ikago39 also investigated the earthquake input energy of an RILD system using both theoretical and experimental approaches. Recently, to achieve the multifrequency control effect of low-frequency structures,40 a novel filter for the mechanical realization of RILD was developed. RTHS is a promising alternative to the dynamic testing of structural systems as it combines physical testing with numerical simulation, thereby significantly reducing the required time, labor, and cost.41-43 In the RTHS method, only critical components, such as rate-dependent components, are physically tested, whereas the remaining elements of the structure are simulated in the numerical domain. Keivan et al.2 conducted RTHS on a 14-story interstory isolation building equipped with a semi-active damper to investigate the performance of an adaptive control algorithm to mimic the behavior of RILD. However, to the best of the authors' knowledge, there is yet to be an experimental study on multistory low-frequency structures equipped with passive RILD devices. The main objective of this study is to investigate the effectiveness of a passive causal RILD device and identify further challenges for implementing RILD for the seismic protection of low-frequency structures. A nine-story seismically isolated building with a fundamental natural frequency of 0.19 Hz equipped with RILD was examined. Maxwell and negative stiffness elements were combined in parallel to implement a passive causal RILD device. A small-scale coil spring unit and oil damper were designed and fabricated to build the Maxwell element. Because the negative stiffness devices that have been developed exhibit nonlinear behavior especially against large deformation,44-47 we reduced the isolator stiffness instead. The remainder of this paper is organized as follows. Section 2 presents the physical implementation of RILD. Section 3 discussed the series of RTHS experiments performed to verify the effectiveness of passive causal rate-independent linear damping (CRILD) device in reducing the dynamic responses of low-frequency structures. Section 4 compares the results of the RTHS and numerical analyses to examine the performance of the passive CRILD device. Finally, Section 5 concludes the study. 2 PHYSICAL IMPLEMENTATION OF RILD Consider a single degree of freedom (SDOF) structure equipped with an ideal RILD subjected to harmonic ground excitation x ¨ g t = Ae iωt , where A, ω, and t are the amplitude of the ground motion, excitation angular frequency, and time, respectively. The steady-state response of the SDOF system can then be expressed as x t = X ω e iωt , where X ω is the displacement amplitude at frequency ω. The damping force of the ideal RILD is expressed as follows48: f RILD = iηk sgn ω X ω (1)where i, η, k, and sgn are the imaginary unit, loss factor of the RILD element, isolator stiffness, and signum function, respectively. In Equation 1, ηk is the loss stiffness and i sgn ω corresponds to the Hilbert transform. To achieve a causal approximation of the Hilbert transform, Keivan et al.35 proposed a first-order all-pass filter with the form: H AP iω = iω − ω T iω + ω T (2)where ω T is the target frequency of the filter. As shown in Figure 1, the amplitude of the filter is equal to unity over all frequencies, and the phase advance is 90° at the target frequency ω T . Therefore, it is expected that the first-order all-pass filter could favorably approximate the Hilbert transform in the vicinity of the target frequency. FIGURE 1Open in figure viewerPowerPoint First-order all-pass filter Luo et al.3 proposed a mechanical configuration to realize passive CRILD, as shown in Figure 2. A coil spring unit and an oil damper, as shown in Figures 3 and 4, respectively, were designed and fabricated to build a Maxwell element in the passive CRILD device.37 The static experiments and dynamic tests of the coil spring unit and oil damper identified the stiffness and maximum friction of the coil spring unit as 14.50 kN/m and 163.91 N, respectively. The equivalent linear viscous damping coefficient of the oil damper is identified as c M = 12.09 kN ⋅ s/m. Table 1 summarizes the specifications of the specimens. An additional equivalent linear viscous damping component c c , which represents the energy dissipated by the inevitable mechanical friction in the coil spring unit identified as 1.83 kN ⋅ s/m, is considered in the physical realization of CRILD, as shown in Figure 5. To distinguish the models with and without additional damping elements, the models shown in Figures 2 and 5 are designated as CRILDNF and CRILD, respectively, where the subscript “NF” implies no friction. To consider the effect of the decreased linear equivalent damping coefficient c c , the responses yielded by CRILDNF should be observed because c c decreases as the isolator displacement increases. FIGURE 2Open in figure viewerPowerPoint Schematic of passive causal rate-independent linear damping (RILD) (CRILDNF). k N is the negative stiffness, and k M and c M are the stiffness and damping coefficients of the Maxwell-type damper, respectively FIGURE 3Open in figure viewerPowerPoint Coil spring unit FIGURE 4Open in figure viewerPowerPoint Oil damper specimen TABLE 1. Specifications of specimens Coil spring unit Oil damper specimen Stiffness 14.5 kN/m Damping coefficient 12.09 kN ⋅ s/m Maximum stroke ±97.5 mm Maximum stroke ±150 mm Outer diameter of each coil spring 42 mm Outer diameter of cylinder 120 mm FIGURE 5Open in figure viewerPowerPoint Schematic of the passive causal rate-independent linear damping (RILD) considering friction in the spring element (CRILD) 3 RTHS 3.1 Parameters of the multistory structure This study investigated a nine-story base-isolated steel structure with a total mass m = 12 , 600 ton and isolator stiffness k base = 18 , 130 kN/m. Assume that the loss factors of a passive RILD device and linear viscous damper (LVD) are 0.4, which is commonly used in the design of seismic isolation in Japan. Then, the damping ratio is as follows: h RILD = h LVD = η / 2 = 0.2 (3)According to Luo et al.,3 k N = − η k base = − 7250 kN / m (4)In this study, we assume linear base-isolation system and superstructure. To consider the potential nonlinear deformation of the isolators during severe earthquakes, which is beyond the scope of this study, the equivalent linear stiffness49, 50 of the isolation layer can be employed to consider the isolator nonlinearity and negative stiffness device. Two factors (gains) were used to fit the resistive force of a small-scale damper in a full-scale structure in the numerical domain. One is a scale factor of 250 to adjust the resistive force of a small-scale specimen to that of a full-scale damper. The other factor of four represents the number of dampers incorporated in the base-isolation layer. Thus, the measured damping force is multiplied by the product of the two factors, that is, 1000, and subsequently fed back to the RTHS loop. As shown in Figure 6, each floor is represented by a lumped mass connected to a spring and dashpot, which represent the stiffness and inherent damping, respectively. Table 2 lists the parameters of the numerical model. Damping is assumed to be proportional to stiffness for the first mode of a superstructure with a damping ratio of 1.54%. Following the common practice in structural design, we neglected the inherent damping of the isolation layer; c base = 0, when CRILD device is incorporated. FIGURE 6Open in figure viewerPowerPoint Schematic of the multidegree of freedom (MDOF) system equipped with causal rate-independent linear damping (CRILD) for a nine-story base-isolated structure TABLE 2. Parameters of the MDOF system for a nine-story base-isolated structure Floor number Mass (ton) Stiffness (kN/m) Damping coefficient(kN · m) Height (m) 9 1260 1,312,000 7590 28 8 1260 1,312,000 7590 25 7 1260 1,312,000 7590 22 6 1260 1,312,000 7590 19 5 1260 1,312,000 7590 16 4 1260 1,312,000 7590 13 3 1260 1,312,000 7590 10 2 1260 1,312,000 7590 7 1 1260 1,312,000 7590 4 Base-isolation layer 1260 18,130 0 1 Abbreviation: MDOF, multidegree of freedom. When we examine a system incorporated with LVD instead of CRILD, c base = η k base / ω 0 , where ω 0 = k base / m total . The modal parameters of the nine-story base-isolated structure are listed in Table 3. The first three participation modes of the nine-story base-isolated structure are shown in Figure 7. TABLE 3. Modal parameters of MDOF system for a nine-story base-isolated structure Mode number Frequency (Hz) Effective mass (ton) Effective mass ratio (%) 1 0.19 1.2595 × 10 4 99.9602 2 1.63 4.6291 0.0367 3 3.18 2.9714 × 10 − 1 0.0024 4 4.67 5.6542 × 10 − 2 4.4875 × 10 − 4 5 6.04 1.6648 × 10 − 2 1.3212 × 10 − 4 6 7.27 6.0818 × 10 − 3 4.8268 × 10 − 5 7 8.31 2.4565 × 10 − 3 1.9481 × 10 − 5 8 9.15 9.9574 × 10 − 4 7.9027 × 10 − 6 9 9.77 3.5550 × 10 − 4 2.8214 × 10 − 6 10 10.15 7.8333 × 10 − 5 6.2169 × 10 − 7 Abbreviation: MDOF, multidegree of freedom. FIGURE 7Open in figure viewerPowerPoint First three participation modes of the undamped multidegree of freedom (MDOF) system for a nine-story base-isolated structure 3.2 Earthquake records The earthquake records51 used for RTHS are listed in Table 4. The Tomakomai 2003 NS (NS: North-South component) record pertains to the 2003 Tokachi-Oki earthquake (Mw 8.0), which was dominated by low-frequency components. The TKY007 NS and Sakishima records were observed during the 2011 Great East Japan Earthquake (Mw 9.0), which caused excessive displacement at the top of high-rise buildings in Tokyo and Osaka. Therefore, these three ground motion records can be categorized as low-frequency ground motions. In Table 4, the duration means the length of the primary shock of each ground motion. The time histories of the Tohoku, Tomakomai, TKY007, and Sakishima earthquake records are shown in Figure 8. The power spectral densities of the earthquake records are presented in Figure 9. TABLE 4. Earthquake records Earthquake Magnitude (Mw) Duration of principal shock (s) Peak ground acceleration (cm/s2) Peak ground velocity (cm/s) El Centro 1940 NS 6.9 53.74 341.65 33.88 Tohoku 2011 NS 9.0 49.46 332.83 47.53 Kobe 1995 NS 6.9 19.98 817.98 91.26 Tomakomai 2003 NS 8.0 290.00 86.68 32.04 Taft 1952 EW 7.3 54.38 175.83 17.76 Hachinohe 1968 NS 7.9 50.98 180.34 37.85 TKY007 NS 9.0 300.00 188.59 24.00 Sakishima 9.0 220.00 33.81 12.51 FIGURE 8Open in figure viewerPowerPoint Time-history records of the (a) Tohoku, (b) Tomakomai, (c) TKY007, and (d) Sakishima earthquakes FIGURE 9Open in figure viewerPowerPoint Power spectral densities of selected earthquake records: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima. f1, f2, and f3 indicate the first three natural frequencies of the MDOF system shown in Table 3 Preliminary numerical analyses were performed to ensure that the test equipment operated within the safety margin while conducting the RTHS. The maximum amplification factors of the selected earthquake records were determined to be 89%, 53%, 48%, 41%, 138%, 82%, 87%, and 93% for the El Centro, Tohoku, Kobe, Tomakomai, Taft, Hachinohe, TKY007, and Sakishima records, respectively. 3.3 Experimental layout of RTHS Figures 3 and 4 show the schematics of the coil spring unit and oil damper, respectively. As shown in Figure 10, the oil damper and coil spring unit are connected in series and incorporated into the physical domain of RTHS. A laser displacement transducer was used to measure the displacement of the oil damper and the shaking table controller to obtain the displacement and acceleration of the actuator. FIGURE 10Open in figure viewerPowerPoint Layout of real-time hybrid simulation (RTHS) 4 COMPARISON OF RESULTS OF THE RTHS AND NUMERICAL ANALYSES In this section, the dynamic responses of the MDOF systems equipped with four types of damping devices (CRILD, ideal RILD, LVD, and CRILDNF) are compared with examine the effectiveness of CRILD for the seismic protection of low-frequency structures, with CRILDNF as the control case with ignored inherent friction in the spring element. The results of the CRILD system were acquired from the RTHS experiments. As the ideal RILD is a noncausal element, frequency-domain analysis, instead of the step-by-step numerical integration in the time domain, was performed. The numerical integrations of the LVD and CRILDNF systems are performed in the time domain. The amplification factors of the earthquake records were set to 80%, 40%, 45%, 30%, 110%, 70%, 70%, and 75% for the El Centro, Tohoku, Kobe, Tomakomai, Taft, Hachinohe, TKY007, and Sakishima records, respectively. 4.1 Frequency response Figure 11 depicts the transfer functions from the ground acceleration to the base displacement and roof floor response acceleration of the MDOF structures equipped with the ideal RILD and LVD. The loss factors of the damping elements are set to 0.4 and 0.6, respectively. The RILD and LVD systems with the same loss factor yielded similar base displacement. Meanwhile, assuming that the first natural frequency of the structure is lower than the dominant frequency of excitations, the transfer function of the roof floor response acceleration suggests that the LVD system may suffer a higher acceleration response than the ideal RILD system. This is attributed to the higher amplification factors of the LVD system than that of the RILD for the high modes. As the loss factor increases, the acceleration response in the high modes increases for LVD, whereas that for RILD remains unchanged. FIGURE 11Open in figure viewerPowerPoint Transfer functions of the multidegree of freedom (MDOF) system: (a) from the ground acceleration to isolator displacement and (b) from the ground acceleration to the roof floor response acceleration 4.2 Response time histories and hysteresis curves of various damping systems Figure 12 depicts the results of the relative displacement of the two MDOF systems equipped with CRILD and ideal RILD devices, respectively, with a loss factor of η = 0.4. The response displacements yielded by the CRILD systems are slightly greater than those of the ideal RILD system. The differences between the displacement time histories of the CRILD and ideal RILD devices are attributed to the phase difference in the transfer function. As depicted in Figure 1, the phase of CRILD only agrees well at the vicinity of the target frequency. The Tomakomai and Sakishima records suffered residual displacement after 180 and 150 s, respectively, which is ascribed to the frictional force in the coil spring unit. FIGURE 12Open in figure viewerPowerPoint Relative displacement of the causal rate-independent linear damping (CRILD) and ideal rate-independent linear damping (RILD) systems (η = 0.4): (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima Figure 13 shows the floor response acceleration of the CRILD and ideal RILD systems. The performance of CRILD in reducing the floor response accelerations is slightly compromised by its limited physical realization compared with ideal RILD, except for the Tomakomai and Sakishima records. Effects of ambient vibration and electronic noise are observed in the results obtained by Tomakomai and TKY007 records. FIGURE 13Open in figure viewerPowerPoint Floor response acceleration of the causal rate-independent linear damping (CRILD) and ideal rate-independent linear damping(RILD) systems: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima Figure 14 depicts the hysteresis curves of the three types of damping devices with the damping force of a single small-scale damper. Owing to the limited physical implementation, such as inevitable friction in the coil spring, and phase differences between the ideal RILD and first-order all-pass filter, the mechanical device cannot accurately mimic the behavior of an ideal RILD. The damping forces of RILD and CRILD are smaller than those of LVD, except for the Tomakomai and Sakishima records. When subjected to low-frequency earthquakes, CRILD yields a high damping force. For instance, CRILD could accurately control a structure with low damping force when subjected to ground motions dominated by high-frequency components, such as the Hachinohe record, whereas it produces an unwanted high damping force when subjected to ground motions dominated by low-frequency components, such as the Tomakomai, TKY007, and Sakishima records. FIGURE 14Open in figure viewerPowerPoint Hysteretic curves of various damping devices: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima 4.3 Peak dynamic responses of multistory structures The peak responses of various types of damping systems are examined in this section. The forces of the four additional damping systems, LVD systems with loss factors of η = 0.4 and η = 0.6, an RILD system with a loss factor of η = 0.6, and CRILDNF, are considered. Five dynamic responses—the peak relative displacement, floor response acceleration, story drift, interstory shear force, and overturning moment—of the nine-story base-isolated structures equipped with CRILD, ideal RILD, LVD, and CRILDNF were compared. To further investigate the effect of installing a negative stiffness device, we also consider two more damping systems with a loss factor of η = 0.4, that is, LVD with negative stiffness (LVD-NS) and the Maxwell-type damper (MD). 4.3.1 Displacement relative to the ground The structures with CRILD and CRILDNF devices exhibit a displacement response relative to the ground, which is slightly greater than those of the ideal RILD and LVD systems with the same loss factor η = 0.4 for all selected earthquake records, as shown in Figure 15. This demonstrates the slightly compromised performance of CRILD in reducing the displacement response. The displacements of the structure relative to the ground are mainly attributed to isolator displacement. Except for the El Centro, Taft, and TKY007 records, the displacement responses of the CRILD system were slightly greater than those of the CRILDNF system. This demonstrates that the friction in the coil spring unit can cause the low-frequency structure to undergo a larger displacement response. FIGURE 15Open in figure viewerPowerPoint Peak relative displacement of the multidegree of freedom (MDOF) systems: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima Generally, the control effects of LVD and ideal RILD on response displacement are similar in all cases. The displacement responses of these two types of damping systems decrease as the loss factor is increased from 0.4 to 0.6. When we compare LVD and LVD-NS systems, Figure 15 shows that the LVD device can reduce the displacement response more effectively in all cases, except for the Tohoku and Kobe records. In the cases of the Tomakomai and Sakishima records, it is evident that the MD device can achieve better control of displacement than the CRILDNF system. Figure 15 also implies that the proposed CRILD system outperforms the LVD-NS system in all cases, except for the Tohoku and Kobe records. To ensure that the test equipment operates within the safety margin while conducting RTHS on CRILD system, the maximum amplification factors of the selected earthquake records are determined to limit the maximum displacement of the actuator to less than 0.12 m. 4.3.2 Floor response acceleration Figure 16 compares the floor response acceleration responses of the different systems. The structures equipped with the CRILD device exhibit a similar floor response acceleration to that equipped with an ideal RILD device. The CRILD device reduced the floor response acceleration more effectively than LVD, except for the Sakishima record. Moreover, there are minimal differences in the performance of CRILD and CRILDNF for all selected records. Based on the mode shape (Figure 7), power spectral densities of excitations (Figure 9), and transfer functions (Figure 11) of the El Centro, Kobe, Taft, and Hachinohe records, the second mode of the structure has the greatest effect on the floor response acceleration response of the CRILD system. FIGURE 16Open in figure viewerPowerPoint Peak floor response acceleration of the multidegree of freedom (MDOF) systems: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima Figure 16 illustrates that the ideal RILD can effectively reduce the floor response acceleration, compared with LVD, for all selected records. For the low-frequency records, such as Tomakomai, TKY007, and Sakishima, similar peak floor response accelerations are noted for the MDOF structure equipped with the four types of damping systems. Further, the ideal RILD device demonstrates a constant performance in reducing the acceleration response when the loss factors are increased from 0.4 to 0.6. In contrast, the floor acceleration response of the LVD system significantly increased in the high-frequency-dominated earthquake records—El Centro, Tohoku, Kobe, and Hachinohe records. Figure 16 demonstrates that the LVD-NS device can more effectively control the floor response acceleration than LVD. Arranging a negative stiffness unit in parallel with the LVD element provides a promising approach for controlling floor response acceleration of low-frequency structures. However, when we remove the negative stiffness in the CRILDNF device, the structure will experience larger floor response accelerations. 4.3.3 Interstory drift Figure 17 shows a comparison of the peak interstory drift of the structure with various types of damping systems. The structures equipped with CRILD and CRILDNF devices exhibit a slightly larger story drift than those equipped with an ideal RILD. Nevertheless, with the same loss factor, the CRILD and ideal RILD devices reduced the story drift more effectively than LVD. Further, as the loss factor increased, the story drift response of the ideal RILD system decreased, whereas that of LVD increases for most of the input ground motions. This indicates the benefits of RILD over LVD in base-isolated structures. An increase in the loss factor of the CRILD device is expected to achieve a similar displacement reduction effect. FIGURE 17Open in figure viewerPowerPoint Peak interstory drift of the multidegree of freedom (MDOF) systems: (a) El Centro, (b) Tohoku, (c) Kobe, (d) Tomakomai, (e) Taft, (f) Hachinohe, (g) TKY007, and (h) Sakishima For all the selected ground motions, the MD system exhibits a larger interstory drift than
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