Innovative baseisolated building with large massratio TMD at basement for greater earthquake resilience


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1 Hashimoto et al. Future Cities and Environment (215) 1:9 DO /s TECHNCAL ARTCLE nnovative baseisolated building with large massratio TMD at basement for greater earthquake resilience Takuya Hashimoto, Kohei Fujita, Masaaki Tsuji and zuru Takewaki * Open Access Abstract Tuned mass dampers (TMD) have been used for the reduction of building responses to wind loading in many highrise buildings. An innovative and resilient baseisolated building with a large massratio TMD is introduced here primarily for earthquake loading in which the large massratio TMD is located at basement. This new hybrid system of baseisolation and structural control possesses advantageous features compared to existing comparable systems with a TMD at the baseisolation story. The TMD stroke can be reduced to a small level with the use of an inertial mass damper and its reaction can be limited to a lower level by detaching its connection to ground. The proposed hybrid system has another advantage that the does not bring large gravitational effect on the building itself. t is demonstrated that the proposed hybrid system is robust both for pulsetype ground motions and longperiod, longduration ground motions which are regarded as representative influential ground motions. Keywords: Earthquake resilience; Baseisolation; Tuned mass damper; Large massratio TMD; nertial mass damper; Basement; Hybrid system ntroduction There is an increasing need and interest of construction of highrise buildings in urban areas. This trend will be accelerated in the future. Highrise buildings and super highrise buildings are required to resist for various external loadings, e.g. wind and earthquake loadings. Enhancement of resilience of such highrise and super highrise buildings after intensive wind and earthquake loadings is a major concern from the viewpoint of the business continuity plan (BCP) which is the most controversial issue in the sound development of society (Takewaki et al. 211, 212b). Tuned mass dampers (TMD) are useful for the reduction of building responses to wind loading and are installed in many highrise buildings all over the world (Soong and Dargush 1997). However it is well known that TMD is not effective for earthquake responses because of its limitation on stroke and realization of large massratio TMD. Nevertheless, some attempts have been made on the introduction of large massratio TMD mainly for earthquake loading (Chowdhury et al. 1987; Feng and Mita * Correspondence: Department of Architecture and Architectural Engineering, Kyoto University, KyotodaigakuKatsura, Nishikyoku, Kyoto , Japan 1995; Villaverde 2; Arfiadi 2; Zhang and wan 22; Villaverde et al. 25; Mukai et al. 25; Tiang et al. 28; Matta and De Stefano 29; Petti et al. 21; Angelis et al. 212; Nishii et al. 213; Xiang and Nishitani 214). Actually several projects are being planned in Japan, e.g. installation of largemass pendulumsystematroofandusageofupperstoriesastmd masses. Recently large massratio TMDs are investigated for baseisolated buildings (Villaverde 2; Villaverde et al. 25; Angelis et al. 212; Nishii et al. 213; Xiang and Nishitani 214). While usual highrise buildings exhibit large displacement around the top story, baseisolated buildings show relatively large displacement around the baseisolation story near ground surface. This property is very advantageous from the view point of mitigation of effect of excessive vertical load due to large massratio TMD (Karee997; Zhang and wan 22; Mukai et al. 25; Petti et al. 21; Nishii et al. 213; Xiang and Nishitani 214). However there still exist several issues to be resolved, e.g. avoidance of excessive vertical load by large massratio TMD, reduction of TMD stroke, reduction of TMD support reactions. 215 Hashimoto et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4. nternational License (http://creativecommons.org/licenses/by/4./), which permits unrestricted use, distribution, and reproduction in any medium, provided yoive appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
2 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 2 of 19 Small massratio TMD on roof Large massratio TMD on roof (Excessive vertical load) Large massratio TMD on roof of baseisolated building (Excessive vertical load) Base isolation for wind for earthquake for earthquake (a) (b) (c) Fig. 1 Conventional model and unrealistic model with excessive vertical load Large massratio TMD at basement (Smart treatment of excessive vertical load) nertial mass damper Base isolation Base isolation solator spring Slide on rail (a) Proposed1 Model (Friction on rail) Use of basement machine as (c) Proposed2 Model (b) Secondary Proposed1 Model (Friction free) Base isolation Slide on rail Fig. 2 Proposed1 model and Proposed2 model (d) Mechanism example of inertial mass damper
3 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 3 of 19 m k1, c1 u 1 1 m 2 2 m2 u2 u z m k 2 u m2 u2 c 2 (a) B Model (b) mass TMD Model (c) New TMD Model m k1, c1 u m k1, c1 u k c 2, 2 m 2 u 2 k, c m 2 k c z 2, 2, 2 u 2 (d) Proposed1 Model (e) Proposed2 Model Fig. 3 Baseisolated building models treated in this paper (a B Model: Simple baseisolated building, b mass TMD Model: Model proposed by Nishii et al. (Nishii et al. 213), c NewTMD Model: Model proposed by Xiang and Nishitani (Xiang and Nishitani 214), d Proposed1 Model: Baseisolated building with largemass ratio TMD at basement, e Proposed2 Model: Baseisolated building with largemass ratio TMD at basement using inertial mass damper for stroke reduction) The purpose of this paper is to propose an innovative system of baseisolated buildings with a large massratio TMD at basement. The most serious issue of effect of excessive vertical load due to large massratio TMD on the main building is avoided by introducing the large massratio TMD at basement which is made possible due to the large displacement of a floor in the baseisolation story near basement. Another issue of large stroke of TMD even in the large massratio TMD is overcome by introducing inertial mass dampers in parallel to the springdashpot system in the TMD system. Fig. 4 Determination of stiffness of TMD (tuning of TMD)
4 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 4 of 19 Baseisolated building with largemass ratio TMD at basement Figure 1(a) shows a conventional system with small massratio TMD on the roof which is effective only for wind loading. On the other hand, Fig. 1(b) presents a highrise building with large massratio TMD on the roof which is believed to be effective for longperiod ground motion and to cause significant vertical load on the building. Consider next a baseisolated building system, as shown in Fig. 1(c), with large massratio TMD on the roof which lengthens the fundamental natural period of the highrise building and also causes large vertical load on the building. The models in Fig. 1(b) and (c) are thought to be unrealistic because of their excessive vertical load. Figure 2(a) indicates the proposed baseisolated building system with large massratio TMD at basement using sliders and rails. This model shown in Fig. 2(a) is called the Proposed1 model. n Fig. 2(a) the large massratio TMD is located on the sliders and rails and in Fig. 2(b) the large massratio TMD is set on the floor just above the baseisolation system. Baseisolated building without TMD Consider a baseisolated building without TMD. This model is called a B model (see Ariga et al. 26). Let k, c, m denote the stiffness, damping coefficient and mass of the baseisolation story in the B model. Furthermore let k 1, c 1, denote the stiffness, damping coefficient and mass of the superstructure. The displacements of masses and m relative ground are denoted by and u, respectively. This model is subjected to the base ground acceleration ü g. The equations of motion for this model can be expressed by m u þ c þ c 1 c 1 _u c 1 c 1 _ þ k þ k 1 k 1 u k 1 k 1 ¼ m ð1þ Conventional baseisolated building with largemass ratio TMD Recently some systems of a baseisolated building with largemass ratio TMD have been proposed. Mukai et al. (25) proposed a newtype active response control system to improve the effectiveness of baseisolated buildings. n this system, the is connected both to a superstructure and the basement (ground). A negative stiffness mechanism is used to amplify the response of the which enables the avoidance of introduction of large massratio TMD. Nishii et al. (213) revised the system due to Mukai et al. (25) by replacing the active damper with negative stiffness with Verocity (m/s) Fig. 5 Simulated longperiod ground motion (T = 7. s) a passive inertial mass damper system. This model is called the mass TMD model in this paper. Although their system is demonstrated to be effective for the reduction of superstructure response, the performance check on the reaction of the TMD system is not conducted. Xiang and Nishitani (214) presented a system for a baseisolated building with a which is located on the baseisolation story level and connected directly to the ground. This model is called the NewTMD model in this paper. They demonstrated that their system is effective for a broad range of excitation frequency and proposed an optimization method for determining the system parameters. Consider an mass TMD model and a NewTMD model as shown in Fig. 3. Let k 2, c 2, m 2 denote the stiffness, damping coefficient and mass of the TMD system. z 2 indicates the inertial mass capacity of the inertial mass damper installed between and ground in the mass TMD model. For later comparison, the mass TMD model and the NewTMD model are explained in the following. The equations of motion for mass TMD model may be expressed by 1 A 1 c þ c 1 þ c 2 c 1 c A c 1 c 1 A _ A m 2 þ z 2 u 2 c 2 c 2 _u 2 1 k þ k 1 þ k 2 k 1 k 2 k 1 k 1 A 1 A A k 2 k 2 u 2 m 2 ð2þ On the other hand, the equations of motion for NewTMD model may be presented by Verocity (m/s) Fig. 6 Simulated pulsetype ground motion (T = 2. s)
5 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 5 of m u c þ c 1 c 1 _u B CB C B CB A c 1 c 1 _ A m 2 u 2 c 2 _u k þ k 1 þ k 2 k 1 k 2 u m B CB C B k 1 k 1 A ¼ u g A ð3þ k 2 k 2 u 2 m 2 Baseisolated building with largemass ratio TMD at basement using inertial mass damper for stroke reduction The equations of motion for a baseisolated building with largemass ratio TMD at basement may be expressed by 1 A 1 c þ c 1 þ c 2 c 1 c A c 1 c 1 A _ A m 2 u 2 c 2 c 2 _u 2 1 k þ k 1 þ k 2 k 1 k 2 k 1 k 1 A 1 A A k 2 k 2 u 2 m 2 ð4þ A baseisolated building, as shown in Fig. 2(c), with largemass ratio TMD at basement using an inertial mass damper for stroke reduction is called the Proposed2 model. A mechanism example of inertial mass dampers is shown in Fig. 2(d) (Takewaki et al. 212a). The equations of motion for this model may be expressed by 1 m þ z 2 z A 1 c þ c 1 þ c 2 c 1 c A c 1 c 1 A _ A z 2 m 2 þ z 2 u 2 c 2 c 2 _u 2 1 k þ k 1 þ k 2 k 1 k 2 k 1 k 1 A 1 A A k 2 k 2 u 2 m 2 ð5þ The model parameters of B Model, Proposed1 Model and Proposed2 Model as shown in Fig. 3 are specified as follows. The same model parameters are used for mass TMD Model and NewTMD Model. The influence of the rail friction on the response of the proposed baseisolation story (m) 2story baseisolation story (m) (a) baseisolation story story 2story.8 5story (b) TMD stroke Reaction of sprong 5 2story Reaction of sprong 1 5story (c) supporting TMD 3 2story story (d) supporting TMD Reaction of inertial mass damper 25 2story Reaction of inertial mass damper 5 5story (e) Reaction of inertial mass damper supporting TMD Fig. 7 Response to simulated longperiod ground motion B Model Proposed1 Model Proposed2 Model mass TMD Model NewTMD Model
6 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 6 of 19 models will be discussed in Section nfluence of rail friction on response of proposed system. The superstructure is a 2story or 5story reinforced concrete building and is modeled into a singledegreeoffreedom (SDOF) model. This modeling into an SDOF model is thought to be appropriate in a baseisolated building. The equal story height of the original building is 3.5 m. The building has a plan of 4 4 m and the floor mass is obtained from 1 3 kg/m 2. The floor mass in each floor is kg. The fundamental natural period of the superstructure with fixed base is T 1 =1.4sfora2 story building and T 1 =3.5 s for a 5story building. The structural damping ratio is assumed to be h 1 = 2. The stiffness and damping coefficient of the SDOF model are computed by k 1 ¼ ω 2 1, c 1 =2h 1 k 1 /ω 1 with the fundamental natural circular frequency ω 1 =2π/T 1. The mass of the baseisolation story is kg. The fundamental natural period of the B model with rigid superstructure is T =5.sforthe2storymodelandT =6. s for the 5story model. The damping ratio of the B model with rigid superstructure is h =.1. The stiffness and damping coefficient of the SDOF model are computed by k ¼ ðm þ Þω 2, c =2h k /ω with the fundamental natural circular frequency ω =2π/T. As for TMD, the mass ratio m 2 / is set to μ =.1 and the inertial mass damper ratio z 2 / is set to η s = 6. The damping ratio is assumed to be h 2 =.3. The stiffness and damping coefficient of TMD are given by k 2 ¼ ðm 2 þ z 2 Þ ω 2 2, c 2 =2h 2 k 2 /ω 2 in terms of the natural circular frequency ω 2 of TMD. The process of determining ω 2 is explained in Section Determination of stiffness and damping coefficient of TMD. Determination of stiffness and damping coefficient of TMD n this section, the procedure of determination of stiffness and damping coefficient of TMD for the proposed model, mass TMD model and NewTMD model is explained. The tuning of TMD is performed by minimizing the response ratio D of the deformation of the base baseisolation story (m) story baseisolation story (m).7 5story story (a) baseisolation story 2story (b) TMD stroke Reaction of sprong 5 2story Reaction of sprong 5 5story (c) supporting TMD 4 2story story (d) supporting TMD Reaction of inertial mass damper story Reaction of inertial mass damper 25 5story (e) Reaction of inertial mass damper supporting TMD Fig. 8 Response to simulated pulsetype ground motion B Model Proposed1 Model Proposed2 Model mass TMD Model NewTMD Model
7 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 7 of 19 isolation story to the base input (displacement amplitude) as shown in Fig. 4. Let us assume the input ground acceleration as ¼ Ae iωt ð6þ The harmonic response of the systems may be expressed by ðu U 1 U 2 Þ T ¼ ω 2 1 M þ iωc þ K ð m A A m 2 A Þ T ð8þ where () T indicates the matrix transpose. The displacement response ratio D can then be defined by ðu u 2 Þ ¼ ðu U 1 U 2 Þe iωt ð7þ D ¼ U A=ω 2 1 ð9þ By solving the equations of motion, the response amplitude may be obtained as where ω 1 is the undamped natural circular frequency of the B model. baseisolation story (m) (a) baseisolation story (b) acceleration acceleration (m/s 2 ) 5 superstructure (m) (c) superstructure (d) TMD stroke relative to ground (m) (e) relative to ground (f) supporting TMD Proposed1 Model (friction free) 2 Proposed1 Model (friction on rail) (g) supporting TMD Fig. 9 nfluence of friction on rail in Proposed1 Model subjected to simulated longperiod ground motion (2story, input period T = 5. s)
8 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 8 of 19 Response reduction performance of proposed system for simple baseisolated building and conventional baseisolationtmd hybrid system Simulated longperiod ground motion and simulated pulsetype ground motion Let us assume the simulated longperiod ground motion in terms of circular frequency ω =2π/T (T: period) as ¼ A sinωt ð1þ Figure 5 shows a simulated longperiod ground motion with T =7.(s). On the other hand, let us assume the simulated pulsetype ground motion as _u p ¼ Ct n e at sinω p t h u p ¼ Ct n e at n i t a sinω p t þ ω p cosω p t ð11þ ð12þ where C: an amplitude coefficient, a: reduction coefficient, n: envelope shape coefficient, ω p =2π/T:circular frequency (see Xu et al. 27). C is determined so as to control the maximum velocity and a is determined from a =.4ω p. The maximum ground velocity is set to.91(m/s) (the maximum velocity of JMA Kobe NS 1995). The period of the pulse wave is specified in the range of ~ 3.(s) with.1(s) as the increment. Figure 6 shows the pulsetype wave of T = 2.(s). baseisolation story (m) acceleration (m/s 2 ) (a) baseisolation story (b) acceleration superstructure (m) (c) superstructure (d) TMD stroke relative to ground (m) (e) relative to ground (g) supporting TMD (f) supporting TMD Proposed1 Model (friction free) Proposed1 Model (friction on rail) Fig. 1 nfluence of friction on rail in Proposed1 Model subjected to simulated longperiod ground motion (5story, input period T = 7. s)
9 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 9 of 19 Response reduction performance of proposed system for simple baseisolated building Figure 7 shows the comparison of various performances under simulated longperiod ground motion among B model, Proposed1 model, Proposed2 model, mass TMD model and NewTMD model. The performances to be compared are (a) baseisolation story, (b) TMD stroke, (c) Reaction of spring supporting TMD, (d) supporting TMD, (e) Reaction of inertial mass damper supporting TMD. The left figures are for 2 story models and the right figures are for 5story models. t can be observed that Proposed1 model can reduce the deformation of baseisolation story by about 38 % compared to B model and Proposed2 model can decrease TMD stroke by about 27 % compared to Proposed1 model. On the other hand, Fig. 8 illustrates the comparison of those performances under simulated pulsetype ground motion. As in Fig. 7, the left figures are for 2story models and the right figures are for 5story models. t can be observed that the deformation of baseisolation story of Proposed1 model and Proposed2 model does not change so much from B model and the baseisolation performance can be kept. Furthermore Proposed2 model can reduce the TMD stroke by about 38 % compared to Proposed1 model. Response reduction performance of proposed system for conventional baseisolationtmd hybrid system t is meaningful to note that, while TMD is connected to the baseisolation floor in the proposed models (Proposed1 model and Proposed2 model), TMD is connected both to the baseisolation floor and ground in the conventional baseisolationtmd hybrid system (mass TMD model and NewTMD model). For this reason the baseisolation story (m) superstructure (m) relative to ground (m) acceleration (m/s 2 ) (a) baseisolation story (b) acceleration (c) superstructure (d) TMD stroke.5 Proposed2 Model (friction free) Proposed2 Model (friction on rail) (e) relative to ground (f) supporting TMD (g) supporting TMD (h) Reaction of inertial mass damper supporting TMD Fig. 11 nfluence of friction on rail in Proposed2 Model subjected to simulated longperiod ground motion (5story, input period T = 7. s) Reaction of inertial mass damper 5
10 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 1 of 19 TMD reactions become relatively large in mass TMD model and NewTMD model. Although the proposed system (Proposed2 model) increases the building response under a longperiod ground motion slightly compared to the system without an inertial mass damper (Proposed1 model), the response is still smaller than that of a baseisolated building without TMD. n addition, the proposed system (Proposed2 model) can reduce the TMD stroke under a longperiod ground motion owing to the inertial mass damper. Furthermore, the proposed system (Proposed2 model) can also reduce the TMD stroke under a pulsetype ground motion owing to the inertial mass damper. t can be concluded that the proposed systems (Proposed 1 model and Proposed2 model) can reduce the TMD stroke and TMD reaction effectively compared to the conventional NewTMD model and mass TMD model for both longperiod ground motions and pulsetype ground motions. nfluence of rail friction on response of proposed system Since the friction on rail in the TMD system could affect the performance of the proposed control system, its influence has been investigated. Although the static friction behavior is usually different from the dynamic one, the static friction coefficient has been treated as the same as the dynamic one. n this paper, the friction coefficient 8 has been used. n order to simulate the friction on rail, an elasticperfectly plastic relation has been utilized and the initial stiffness has been specified as 1 1 (N/m). Figure 9 shows the influence of friction on rail in Proposed1 Model subjected to simulated longperiod baseisolation story (m).5 acceleration (m/s 2 ) (a) baseisolation story (b) acceleration superstructure (m) (c) superstructure (d) TMD stroke relative to ground (m) (e) relative to ground (f) supporting TMD Proposed1 Model (friction free) Proposed1 Model (friction on rail) (g) supporting TMD Fig. 12 nfluence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (2story, input period T = 2. s)
11 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 11 of 19 ground motion (2story, input period T = 5. s). Figure 1 illustrates the influence of friction on rail in Proposed1 Model subjected to simulated longperiod ground motion (5story, input period T =7. s). Furthermore Fig. 11 presents the influence of friction on rail in Proposed2 Model subjected to simulated longperiod ground motion (5story, input period T =7.s). On the other hand, Fig. 12 shows the influence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (2story, input period T = 2. s). Figure 13 illustrates the influence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (5story, input period T = 2. s). Furthermore Fig. 14 presents the influenceoffrictiononrailinproposed2modelsubjected to simulated pulsetype motion (5story, input period T = 2. s). t can be observed that, while the reactions of TMD supports and TMD stroke are affected slightly inadampedprocess,thesuperstructureresponseand baseisolation story response are not affected so much. t can be concluded that, although the frictions of TMD mass on rail in the proposed systems reduce the TMD stroke for both longperiod ground motions and pulsetype ground motions, those do not affect so much on the building response. Reduction of TMD stroke using various methods n the large massratio TMD, the reduction of stroke of TMD is a key issue. Figure 15 shows several attempts to implement it. Proposed1 model is a basic model. As its derivatives, Proposed11 model (detuning), Proposed12 model (increased damping) and Proposed13 model (increased ratio) are considered. Furthermore Proposed2 model is a derivative of Proposed1 baseisolation story (m) superstructure (m) (a) baseisolation story (b) acceleration acceleration (m/s 2 ) (c) superstructure (d) TMD stroke relative to ground (m) (e) relative to ground (f) supporting TMD (g) supporting TMD Proposed1 Model (friction free) Proposed1 Model (friction on rail) Fig. 13 nfluence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (5story, input period T = 2. s)
12 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 12 of 19 baseisolation story (m) superstructure (m) relative to ground (m) (a) baseisolation story (b) acceleration acceleration (m/s 2 ) (c) superstructure (d) TMD stroke (e) relative to ground (f) supporting TMD (g) supporting TMD (h) Reaction of inertial mass damper supporting TMD Fig. 14 nfluence of friction on rail in Proposed2 Model subjected to simulated pulsetype motion (5story, input period T = 2. s) Proposed2 Model (friction free) Proposed2 Model (friction on rail) Reaction of inertial mass damper model and includes an inertial mass damper in TMD. The mass TMD model is also a derivative of Proposed1 model and has an inertial mass damper between TMD mass and ground. Table 1 shows design conditions on TMD parameters in abovementioned several models for stroke reduction. The TMD parameters have been determined so as the reduction of TMD stroke from Proposed1 model under a longperiod ground motion to be almost equivalent. Figure 16 shows the responses ((a) deformation of baseisolation story, (b) acceleration, (c) deformation, (d) TMD stroke, (e) TMD displacement relative to ground (f) supporting TMD, (g) supporting TMD, (h) Reaction of inertial mass damper supporting TMD) to a longperiod ground motion and Fig. 17 shows those responses to a pulsetype ground motion. The comprehensive comparison of the response characteristics in Fig. 16 will be shown in Fig. 2 and Table 2. A similar comparison of the response characteristics in Fig. 17 will be shown in Fig. 21 and Table 2. Figure 18 shows the comparison with B model under a pulsetype motion and Fig. 19 indicates the comparison with Proposed1 model under a pulsetype motion. The comprehensive comparison of the response properties in Figs. 18 and 19 will be shown in Fig. 21 and Table 2. Figure 2 illustrates the response comparison under a longperiod ground motion. The maximum responses with respect to the input period have been taken. t can be observed that, while mass TMD model is superior to Proposed2 model in superstructure responses to some extent, Proposed2 model is superior to mass TMD model in TMD reactions. On the other hand, Fig. 21 shows the response comparison under a pulsetype ground motion
13 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 13 of 19 m k1, c1 u m u 2 (a) Basic model (Proposed1 Model) m k1, c1 u m k1, c1 u m k1, c1 u m 2 m 2 k, c 2 2 u 2, k2 c2 u 2 m u 2 (b) Proposed11 Model (detuning) (c) Proposed12 Model (increased damping) (d) Proposed13 Model (increased ratio) m m 2 k1, c1 u (e) Proposed2 Model (with inertial mass damper), z u Fig. 15 Several proposed models and conventional model for TMD stroke reduction m 2 2 m2 u2 u z 2 (f) mass TMD Model (conventional model with inertial mass damper) Table 1 Design conditions on TMD parameters in several models for TMD stroke reduction Proposed1 Model as basic model Proposed11 Model (detuning) Proposed12 Model (increased damping) Proposed13 Model (increased TMD massratio) Proposed2 Model (with inertial mass damper) ratio μ 1 % 1 % 1 % 26.7 % 1 % 1 % nertial mass damper ratio η s TMD damping ratio h 2 Tuning ratio γ mass TMD Model (conventional model with inertial mass damper)
14 Hashimoto et al. Future Cities and Environment (215) 1:9 Page 14 of 19 Proposed1 Model Proposed11 Model Proposed12 Model Proposed13 Model Proposed2 Model mass TMD Model baseisolation story (m) (a) baseisolation story relative to ground (m) 2..5 acceleration (m/s 2 ) (b) acceleration (f) supporting TMD superstructure (m) (g) supporting TMD (d) TMD stroke (e) relative to ground Fig. 16 Response to longperiod ground motion (c) superstructure Reaction of inertial mass damper (h) Reaction of inertial mass damper supporting TMD Table 2 Response comparison among proposed models and conventional models under longperiod and pulsetype ground motions Proposed11 Model Proposed12 Model Proposed13 Model Proposed2 Model mass TMD Model Longperiod ground motion baseisolation story 〇 acceleration superstructure TMD stroke Similar reduction from Proposed1 Model relative to ground 〇 〇 supporting TMD supporting TMD Reaction of inertial mass damper supporting TMD Pulsetype ground motion baseisolation story acceleration superstructure TMD stroke 〇 〇 relative to ground 〇 〇 supporting TMD supporting TMD Reaction of inertial mass damper supporting TMD : excellent performance, 〇 : good performance, : fair performance, : ordinary performance : small change from Proposed1 model NewTMD Model
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