1stPan-American Congress on Computational Mechanics – PANACM 2015 XI Argentine Congress on Computational Mechanics – MECOM 2015 S. Idelsohn, V. Sonzogni, A. Coutinho, M. Cruchaga, A. Lew&M. Cerrolaza (Eds)
CONCEPTS OF DAMPERS FOR EARTHQUAKE PROTECTION OF EXISTING BUILDINGS AND FOR DISPLACEMENTS RESTRAINTS IN SEISMICALLY ISOLATED BUILDINGS MIKAYEL G. MELKUMYAN Armenian Association for Earthquake Engineering 1Charents str., 0025, Yerevan, Armenia mmelkumi@yahoo.com
Key words: Tuned Mass Damper, Isolated Upper Floor, Structural Concept, Earthquake Response Analysis, Dynamic Tests, First Application. Abstract. Tuned Mass Damper (TMD) is one of the methods, known as a passive vibroprotecting device. The attempt to find the optimal parameters of TMD in the form of an additional flexible upper tenth floor (AFUF) in a 9-story frame building is presented. The efficiency of a single mass damper tuned to the first mode of building vibration is not very high. Therefore, three dampers tuned to the first three vibrations modes of the building are considered much more effective. However, solution of TMD in the form of AFUF contains some deficiencies, which are described in the paper. Therefore, the author has suggested providing flexibility to the damper using laminated rubber-steel bearings. In such case the AFUF will turn into an additional isolated upper floor (AIUF). Results of the earthquake response analyses and of dynamic testing of the existing 9-story apartment frame building before and after erection of AIUF are given. Paper also presents a new concept of dynamic damper (DD) to restrict the displacements of seismically isolated buildings. Since the maximum displacement occurs at the level of isolators the proposed damper as a mass-spring subsystem attached either above or below the isolation interface. It is suggested to use the pavement around the building to create the damper in low-story structures. Other variant of damper is suggested for the large multistory buildings. In both cases the spring of the damper is represented by laminated rubber bearings, which work in one case under the tension and in another – under the compression forces. First real application of DD in construction of a seismically isolated residential house is described in the paper. 1
INTRODUCTION
There are more than 40 buildings in Armenia built, retrofitted or under construction employing the seismic (base and roof) isolation technologies, mostly using locally manufactured bearings with low or medium damping made of neoprene thus putting Armenia at a top rank in terms of the number of seismic isolated buildings per capita [1]. The effectiveness of an appended mass-spring system in reducing the dynamic response of a structure has been known for a long time. Numerous investigations and implementations of this idea for fixed-base buildings have been made [2,3,4]. In such buildings, the damper is
Mikayel G. Melkumyan
usually placed in an upper floor in order to experience a larger acceleration for efficiently mobilizing itself and absorbing the energy in the system. In the case of a base isolated structure the damper must be attached immediately at the level of the isolation system. One option for reducing the displacement demand on the isolation system is to provide supplemental damping. This, however, may increase the instructure accelerations [5]. A new type of damper to restrict the displacements of seismically isolated buildings called Dynamic Damper (DD) was developed and proposed by the author of this paper [6]. The name “dynamic damper” or “dynamic absorber” is applied when the auxiliary mass system has little damping [2]. It is suggested to use as the mass of the DD the perimeter pavement around the building which is separated from the superstructure and hung to it by means of laminated rubber bearings. The stiffness and the mass of the DD should be chosen such, that the period of vibration of the DD is equal to that of the isolated building. Such damper will allow to decrease the horizontal displacements and also to simplify the isolation system itself. The suggested structural system of the DD also increases the overturning resistance of the isolated building [6,7]. 2
BACKGROUND AND LINEAR ANALYSES OF A BUILDING WITH AND WITHOUT TMD IN THE FORM OF AN ADDITIONAL UPPER FLOOR
Basically TMD is a single-degree-of-freedom appendage of the primary structure [8]. Dampers have been widely investigated in connection with seismic protection problems [8,9,10]. The natural frequency of TMD should be equal to the forced vibration frequency of the structure to be protected. Therefore, if the first vibration mode is the most significant one during earthquakes, then the natural frequency of the damper should be equal to the first mode frequency of structure vibration [11]. An additional upper floor for the buildings has been proposed as a vibration damper – TMD [12,13] and it could be erected on the existing buildings to increase their seismic resistance, without requiring the tenants to leave the building. The attempt to find the optimal parameters of TMD in the form of an additional flexible upper tenth floor (AFUF) in 9-story frame buildings, using acceleration time histories of various earthquakes is presented below. The equations of the forced vibrations of a cantilever beam with masses concentrated at the floor levels are given by the formula [11]: mk yk y0 ak yk yk 1 k ak y k y k 1 ak 1 yk 1 yk k 1ak 1 y k 1 y k 0,
(1)
where mk, ak, yk are the mass, stiffness and displacement of the kth floor of the building, mr=m10, ar=a10, yr=y10 are the mass, stiffness and displacement of the TMD-AFUF, k / is the coefficient of viscous damping of the kth floor, and y0 (t ) is the ground acceleration. The values of floors’ stiffness and mass of the investigated building are as follows: a1 = a2 = … = a9 = 897000 kN/m; m1 = m2 = … = m8 = 360
kN s 2 m
; m9 = 430
kN s 2 m
. At k=0 the
periods of the three vibration modes of the building without TMD are equal to: T1 = 0.778 s, T2 = 0.261 s, T3 = 0.159 s. The building with TMD was analyzed using 12 acceleration time histories of strong earthquakes with the purpose to obtain the minimal values of the base shear
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forces, to determine corresponding optimal values of = mr/m1 and d = ar/a1, and to compare the received results with those calculated for the building without TMD (Tab. 1). Table 1: Optimal parameters of TMD and base shear forces of a 9-story building analyzed by 12 acceleration time histories with and without TMD
Earthquakes Ferndale, USA 7.10.1951, 44W Ferndale, USA 7.10.1951, 46E Ferndale, USA 21.12.1954, 44W Ferndale, USA 21.12.1954, 46E Ulcinj-2, Yugoslavia 15.04.1979, N-S Ulcinj-2, Yugoslavia 15.04.1979, N-E Herceg Novi, Yugoslavia 15.04.1979, N-S Herceg Novi, Yugoslavia 15.04.1979, N-E Ferndale, USA 3.10.1941, H60 Hollister, USA 9.03.1949, H21 Eureka, USA 21.12.1954, H10 Taft, USA 12.01.1954, H70
Optimal parameters determined for each time history d 0.50 0.0150 1.25 0.0334 0.50 0.0100 1.00 0.0075 1.00 0.0075 1.25 0.0334 1.00 0.0265 1.25 0.0334 0.75 0.0334 0.50 0.0100 0.50 0.0200 0.50 0.0120
Base shear forces (kN) of the building with TMD 1600 2740 7380 8600 3900 7260 6200 5200 1318 2240 5620 1100
without TMD 2680 4320 11220 12560 5180 11700 10080 7780 1856 3900 8400 2040
The results are showing that AFUF reduces the shear forces by about 35% in average. Seismic loads and shear forces, as well as displacements along the height of the building for both cases are shown in Figure 1. The mean values of the optimal parameters derived from Table 1 are the following: = 0.83 and d = 0.02. Thus, the mass of TMD is equal to about 9% of the total mass of the building and its stiffness is about 50 times less than the stiffness of the building’s typical floor. However, three dampers tuned to the first three vibrations modes of the building are considered much more effective and, therefore, a building structural solution with three TMDs has been proposed. When analyzing any building with TMDs, the number of vibration modes that should be taken into account is equal to the number of TMDs, with addition of at least the next three modes [10,11]. Namely, for the buildings with three dampers as it is schematically illustrated in Figure 2 at least six vibration modes should be encompassed in the analysis. The multi-version analyses of such structure allowed to conclude that in this case optimal stiffness and mass correlations of dampers could be found that enable significant reduction of shear forces and displacements (for about 2 times) compared to the building without TMDs. Reduction of lateral forces and displacements in the building with TMD takes place due to increase of vibration period of the whole system (building plus the TMD) and decrease of the first mode participation factors. However, a new type of second vibration mode appears and becomes prevailing, which results in the TMD oscillations in anti-phase relative to the building along the whole duration of the earthquake [12,13].
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Figure 1: Seismic loads (a), shear forces (b) and displacements (c) of the 9-story building without (solid line) and with (dashed line) the TMD analyzed by the 9.03.1949, H21 Hollister acceleration time history
Figure 2: Schematic of the 9-story building with three TMDs tuned to its first three natural frequencies (a) and six vibration modes taken into account (b) in the analysis of the building
3 JUSTIFICATION OF TRANSITION FROM THE CONCEPT OF FLEXIBLE UPPER FLOOR TO THE CONCEPT OF ISOLATED UPPER FLOOR The TMD in the form of AFUF considered above was implemented on the R/C 9-story frame building (Fig. 3). The AFUF represents a structure made of steel columns supporting a thick R/C slab. This building was tested using a powerful vibration machine installed on the slab of the 9th floor in two stages – before and after erection of AFUF [12]. Nevertheless, it became obvious that such a structural solution of AFUF contains some deficiencies from the practical point of view. In order to rigidly connect steel columns to the structural elements of the building, these columns should have sufficiently big cross-sections. But in this case the only way to provide the needed flexibility to the AFUF is to increase the height of steel columns (more than 4 m). However, this measure on one side reduces the resistance of AFUF against wind and on the other side raises its gravity center very high above the existing building. Therefore, during strong ground motions the flexible upper floor, though protecting the existing building, may itself suffer severe damages or even be destroyed causing damages to the building. Another deficiency is that no exterior and interior walls shall be constructed around and inside the space of the flexible floor as they will restrict its large horizontal displacement. Because of that and the possibility of partial or total destruction of AFUF during strong earthquakes it cannot be occupied and does not possess sufficient reliability. All the above justifies the necessity to change the conceptual solution of this floor while keeping its idea. The author of this paper has suggested providing flexibility to the damper using laminated rubber bearings [10,13]. Obviously, in such case the known AFUF will turn into an additional isolated upper floor – AIUF (Fig. 4). Thus, the thin flexible columns are changed to seismic isolation LRBs and the slab, representing the mass of the flexible floor, is also changed to a whole upper floor connected to the existing building via laminated rubber bearings (LRBs).
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Figure 3: General view of the 9-story building with the TMD-AFUF
Figure 4: Change of the concept of the additional upper floor from flexible to isolated
It is important to note that in the proposed solution the R/C slab of AIUF is constructed right above the LRBs and comprises the largest portion of the damper-AIUF mass. Therefore, the gravity center of the damper in this new structural solution is very close to the existing building. Actually, AIUF itself above the isolation interface is a rigid structure, which being supported by LRBs undergoes practically no deformations during the earthquakes. Consequently, the suggested new concept of a TMD creation on top of the existing building allows not only to increase its seismic resistance and reliability of the whole system, but also to enlarge its useful space, which can be used for many different purposes. 4 NON-LINEAR SEISMIC RESPONSE ANALYSIS AND DYNAMIC TESTS OF THE 9-STORY FULL-SCALE EXISTING BUILDING BEFORE AND AFTER ERECTION OF AIUF The method of AIUF was used in earthquake protection design and implementation for two existing R/C 9-story standard design buildings (Fig. 5). A special structure connecting the AIUF to the building was developed (Fig. 6). At the level of upper truss belts R/C slab is designed. The roof and the exterior walls of the AIUF were designed using light, “sandwich� type elements (Fig. 7). Free vibrations periods for a large number of this type of buildings were determined by the measurements of micro oscillations. The following results were obtained: first mode vibration period in transverse direction (along the R/C frames with weak beams and shear walls) Ttrans= 0.48 s in average, and in longitudinal direction (along the R/C frames with strong beams) Tlong= 0.59 s in average. Similar results for undamaged buildings are indicated in [14]. Design model of the building is presented in Figure 8. Seismic response analysis was carried out for the building with and without AIUF, using degrading tri-linear model for columns and bilinear model for rubber bearings, as well as the Melkumyan model for shear walls [15], and using 7.12.1988, X direction Spitak Earthquake accelerogram scaled to 0.4g. The main results of non-linear seismic response analysis are given in Figure 9 and Table 2. The small scale of Figure 9 makes it hard to see the behavior of LRBs. Therefore, hysteresis loops for one LRB in a larger scale are presented in Figure 10. From the obtained results it can be seen that the R/C columns and shear walls of the building protected with TMD are mainly in the cracking stage, although yielding does occur in the shear walls of the lower four floors. Comparative analysis of the same building without TMD
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shows that under the action of the same accelerogram the columns are in the yielding and shear walls are in the ultimate stages of deformation [10,11].
Figure 5: General views of the two existing R/C 9-story apartment buildings protected by AIUF
Figure 6: Steel rigid trusses constructed on the top of 9story building and at the bottom of AIUF providing reliable connection of AIUF with the building by LRBs
Figure 7: The inner space of AIUF at the construction completion stage
Figure 8: Design model of 9-story building protected by AIUF
150
Horizontal force, kN
100
50
0
-50
-100
-150 -120
without AIUF with AIUF without AIUF with AIUF Figure 9. Restoring force - floor drift relationships for each floor of the building without and with AIUF
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-80 -40 0 40 80 Horizontal displacement, mm
120
Figure 10. Force-displacement relationship for a rubber bearing of AIUF
Mikayel G. Melkumyan
Thus, the TMD provides sufficient earthquake protection to the building. The non-linear seismic response analysis proves that with TMD (AIUF) seismic loads experienced by the building could be reduced along the height of the building by about 2.5 times in average. Table 2: The values of horizontal seismic shear forces and stages of deformation obtained by non-linear seismic response analysis of R/C 9-story apartment building with and without AIUF
Story
1
2 3 4 5 6 7 8 9 AIUF Building without AIUF Seismic shear forces, kN 11601 11286 10589 9981 9548 9241 8803 7851 4723 In columns Y Y Y Y Y Y Y C C Stages of deformation In shear walls U U U U U Y U Y Y Building with AIUF Seismic shear forces, kN 8332 8199 7154 6603 5130 4014 2927 1720 958 1315 In columns C C C C C C C E E E Stages of deformation In shear walls Y Y Y Y C C C C E E – elastic, C – cracking, Y– yielding, and U – ultimate stages of deformation
It was also decided to conduct dynamic tests of these buildings in two stages: first without AIUF, and then with it in resonance mode using unprecedented by its power vibration machine, which provided excitation of inertial horizontal loads allowing imitation of the design level seismic impact [13]. In the building test without AIUF the design intensity (VII by MSK-64 scale) was exceeded for about 6%. Along with that no damage was observed in the bearing structures. This means the building is capable to withstand reliably the intensity VII impact [10, 13]. Testing of the building with AIUF again was held in resonance regime, but in two vibration modes: AIUF and the building oscillate in the same phase (mode I/1), and AIUF oscillates in the anti-phase to the building (mode I/2). Comparison of the obtained shear forces at the ground floor level and displacements at the level of 9th floor slab have shown that thanks to the AIUF shear force and displacement are reduced by factors of 1.76 and 2.2, respectively. At the same time the drift of AIUF, or specifically the LRB displacement, exceeds the maximum drift of a story in the building by a factor of 4.3. However, this does not prevent using the AIUF space for various purposes, since its structures remain almost undeformed. That is why AIUF compares favorably with AFUF. 5 STRUCTURAL CONCEPTS OF DAMPERS FOR DISPLACEMENTS RESTRAINTS IN SEISMICALLY ISOLATED BUILDINGS A 4-story base isolated apartment building constructed in Armenia in 1997-1998 is considered below as an example. For this base isolated building the location of a dynamic damper (DD) has been set at the level of the isolation system. With this purpose it was suggested to separate the blind area pavement around the building from the superstructure and then connect it to the superstructure via LRBs. Thus, the DD would consist of the mass (the mass of the pavement) and the spring (LRBs), and represent a single-degree-of-freedom system hung to the superstructure (Fig. 11).
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However, the damper can be provided as a mass-spring subsystem attached either above or below the isolated floor of the building [10]. If the building represents a large multistory multifunctional system, which is different than the above mentioned apartment building, then of course the suggested dynamic damper could be modified. First of all, the damping factor for the isolation interface of the large building, as well as for the bearings of the damper will increase. In this case the dynamic damper will transform to a tuned mass damper (TMD). Second, its location in the building will require special consideration as the mass of such a TMD will be significantly bigger. For this case the suggested structural concept is shown in Figure 12. Obviously, that in contrast to the rubber bearings of the DD, which are working under the tension forces, the TMD’s rubber bearings will work under the compression forces.
TMD
Figure 11: Structural concept of the DD for base isolated building
TMD
Figure 12: Schematic of a base isolated structure with TMD
One can imagine various functions for such a subsystem: an exercise room, a swimming pool, parking space, utilities room, as long as the mass remains relatively constant in time and large displacement can be accommodated. Proposed TMD scheme has the advantage of increasing the capacity of the base isolated building against overturning forces [7]. 6 FIRST APPLICATION OF THE DYNAMIC DAMPER IN CONSTRUCTION OF SEISMICALLY ISOLATED RESIDENTIAL HOUSE In order to identify the parameters of DD to be applied to a residential house it is assumed that a new mass is added to this system at the level of the isolation interface (Figs. 13, 14). Let us denote that d is the frequency of vibrations of the damper’s added mass, β=md/m – the ratio of the damper’s mass md to the mass of the main isolated system m; 0, 1 and 2 – the frequency of the main isolated system, and the first and second frequencies of the newly created system’s free vibrations, i.e. the main system plus the damper, and n – is a damping factor. The problem is to choose the frequency of the damper d so that at the given values of 0, n and β the value of the displacement of the main isolated system after adding the DD would be minimal in comparison with its value before adding the DD for the whole duration of the earthquake. This is a very complicated task, which does not have a common solution for a system with an arbitrary initial frequency 0, subject to an earthquake. For solving this problem it is necessary to choose a numerical value of β for the given 0, to present the frequency of damper d in the form of d=0 and to substitute it in the differential equation. This will allow determining 1 and 2 through the values and 0. Then giving different
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values to , it is possible to reach the minimum value of the displacement. The magnitude of factor , which corresponds to the minimum value of displacement, together with the value β will become a basis for designing the DD [16]. upper beam of the isolation system 70 205 75
upper column above the seismic isolation rubber bearing
laminated rubber bearing of DD
seismic isolation rubber bearing
15
2
10
20
300
seismic isolation rubber bearing
A
350 cm
500 B
500 C
78
60 20
15
102
20
lower column under the seismic isolation rubber bearing shear wall of the basement
300 30
20
40 40 150 20 30
50
laminated rubber bearing of DD
pavement around the building
18
60
soil
18
50 D
mass of DD in the form of continuous R/C beam around the building
Figure 13: Vertical elevation of the base isolated residential house and details of DD
retaining wall around the building
Figure 14: Three-dimensional view of the seismic isolation system and the DD
It was suggested to use the space under the perimeter pavement around the building for creation of DD connecting it to the pavement by LRBs installed with certain spacing. The mass of DD in its turn is designed as a continuous R/C beam around the whole perimeter of the building (Fig. 15). This mass in case of a low-story building should be around 3-5% of the mass of the superstructure. As it is mentioned above, the isolated building with DD will have two main modes of vibrations: when the DD oscillates in the same phase with the building and when it oscillates in anti-phase to the building. It is this second mode that becomes prevailing and due to this phenomenon horizontal displacements and forces are reduced. a.
b.
Figure 15: Pavement around the building before placing the reinforcement and casting the concrete (a) and the final view of DD as a continuous beam hung to the pavement by means of laminated rubber bearings (b)
7 NON-LINEAR EARTHQUAKE RESPONSE ANALYSIS OF THE RESIDENTIAL HOUSE WITH AND WITHOUT DYNAMIC DAMPER The building was analyzed by SAP2000 non-linear program by a three-dimensional design model (Fig. 16) using the above mentioned acceleration time history recorded at Ashotsk station. Experimentally obtained characteristics of seismic isolation rubber bearings were as follows: total initial stiffness of sixteen rubber bearings – 1365.8 kN/cm, strain hardening (effective) stiffness – 129.6 kN/cm, yield strength – 273.2 kN, yield displacement – 0.2 cm.
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The analysis was carried out for different values of the DD weight (or β and ) in order to identify the most effective parameters leading to maximum reduction of the isolation system displacement. The range of β (the ratio of the DD weight to the weight of the building) varied from 0.42% to 7.01%. Some results of analysis of the building with and without DD are given in Table 3 and in Figure 17.
Displacement, mm
250
YDD
200 150
Displacement of the structure without DD
100
YS 50 0 0
1
2
3
4
5
6
7
8
=WDD/WS , %
Figure 16: 3D design model of the base isolated residential house
Figure 17: Horizontal displacements-factor β relationships for the structure with and without DD
Table 3: Results of the non-linear earthquake response analysis of the residential house with and without DD
WDD, weight YS, displacement YDD, displacement T1, period of the T2, period of the WDD/WS, % of DD, kN of structure, mm of DD, mm first mode, sec second mode, sec Without DD, weight of structure WS = 13900 kN 127.14 2.07 With DD 974.98 7.01 70.37 115.50 2.80 1.97 882.18 6.35 67.21 112.51 2.72 1.96 710.50 5.11 62.93 107.58 2.57 1.93 612.63 4.41 62.87 103.69 2.48 1.90 522.00 3.76 62.82 99.98 2.41 1.87 435.62 3.13 65.85 107.79 2.35 1.83 362.50 2.61 72.40 128.37 2.30 1.78 293.62 2.11 80.00 149.18 2.26 1.73 232.00 1.67 90.16 166.21 2.23 1.67 177.62 1.28 98.62 177.62 2.21 1.61 130.50 0.94 105.54 183.82 2.19 1.56 90.62 0.65 110.80 186.29 2.18 1.51 58.00 0.42 114.56 186.56 2.17 1.46
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The obtained results show that the suggested structural concept of DD is very effective and leads to significant reduction of the seismically isolated structure’s horizontal displacements. Maximum reduction occurs at the values of factor β (WDD/WS) varying from 3.76% to 5.11%. For this range of factor β, the factor (DD/0) in average is equal to 1.4. DD with these parameters reduces the horizontal displacements and the shear forces at the level of isolation system by 2 times in average. Table 3 also suggests that the building’s period of the first mode of vibrations without DD is between the periods of the new first and second modes of vibrations of the building with DD and differs from them by +0.42 sec and -0.17 sec. 8
CONCLUSIONS -
-
-
-
Tuned mass dampers as additional upper floors in the form of AFUF or AIUF are suggested and presented. The efficiency of a single mass damper tuned to the first mode of building vibration is not very high. Three dampers tuned to the first three vibrations modes of the building are considered much more effective as in this case optimal stiffness and mass correlations of dampers could be found that enable significant reduction of shear forces and displacements (for about 2 times) compared to the building without TMD. Deficiencies of AFUF are described and, thus, providing flexibility to the damper using LRBs is suggested. Transition from the concept of AFUF to the concept of AIUF is justified. The non-linear seismic response analysis proves that with AIUF, acting as a TMD, seismic loads (the strain-stressed state level) experienced by the building could be reduced along the height of the building by about 2.5 times in average. Dynamic testing of the existing 9-story building before and after erection of AIUF allows to conclude that the proposed AIUF method leads to upgrading earthquake resistance of buildings and that AIUF brings to reduction of shear force at the ground floor level by a factor of 1.76 and at the same time the displacement at the 9th floor slab level decreases 2.2 times. The proposed new concept of a damper as a mass-spring subsystem attached either above or below the isolation interface is an effective means to restrict the displacements of seismically isolated buildings. The spring of the damper is represented by LRBs. Non-linear earthquake response analyses of the base isolated buildings with and without DD show that due to application of the suggested structural solutions of DD significant (about 2 times) reduction of the horizontal displacements and shear forces at the level of isolation system takes place. First real application of DD in construction of a seismically isolated residential house is described.
REFERENCES [1] Melkumyan, M. Innovative seismic isolation technologies and new structural solutions
developed in Armenia for construction of new and retrofitting of existing buildings. “MENSHIN” Journal of Japan Society of Seismic Isolation (2014)83:33-48.
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[2] Reed, F. Dynamic vibration absorbers and auxiliary mass dampers. In C.M. Harris and
Ch.E. Crede (eds), Shock and Vibration Handbook. McGraw-Hill (1961):6-1- 6-38. [3] Warburton, G. Optimum absorber parameters for various combinations of response and
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excitation parameters. Earthquake Engineering and Structural Dynamics (1982)10:381401. Melkumyan, M. Non-linear seismic response analysis of 9-story building protected with an AIUF. Proceedings of the Fourth European Conference on Structural Dynamics, Prague, Czech Republic (1999)2:1165-1170. Kelly, J. The role of damping in seismic isolation. Earthquake Engineering & Structural Dynamics (1999)28:3-20. Melkumyan, M. The state of the art in structural control in Armenia and proposal on application of the dynamic dampers for seismically isolated buildings. Proceedings of the Third International Workshop on Structural Control, Paris, France (2000):65-373. Taniguchi, T., Der-Kiureghian, A. and Melkumyan, M. Effect of tuned mass damper on displacement demand of base-isolated structures. Engineering Structures (2008)12(30):3478-3488. Melkumyan, M. Base and roof isolation for earthquake retrofitting and protection of existing buildings in Armenia. Proceedings of the International Symposium on Seismic Risk Reduction, Bucharest, Romania (2007):593-600. Palazzo, B., Petti, L. and De Iuliis, M. A passive robust control strategy: base isolation and tuned mass damping. Proceedings of the Third European Conference on Structural Control, Vienna, Austria (2004):51-207 - 51-210. Melkumyan, M. New Solutions in Seismic Isolation. LUSABATS, Yerevan, (2011). Melkumyan, M. Formation of the Dynamic Design Models for Seismic Response Analysis of Reinforced Concrete Buildings and their New Structural Solutions. (in Russian) Yerevan, (1993). Melkumyan, M. Experience of application of modern seismic protection systems. In E. Khachian, T. Margaryan, S. Karapetyan and G. Azizyan (eds), Spitak Tragedy should not Happen Again. Voskan Yerevantsy, Yerevan (1998):193-205. Melkumyan, M. Dynamic tests of the 9-story R/C full-scale building with an additional isolated upper floor acting as vibration damper. Proceedings of the 3rd European Conference on Structural Dynamics, Florence, Italy (1996), Vol. 1:557-560. Kobayashi, H. and Ohtani, K. Dynamic properties of ground and buildings in Armenia based on measurement of micro tremors. Report of Japan Disaster Relief Team on Earthquake at Spitak, Armenia. Japan International Cooperation Agency, Tokyo, Japan, (1990):203-224. Melkumyan, M., Inoue, T., Kumazawa, F., Nakano, Y. and Okada, T. Hysteresis model for the shear behavior of R/C multistory frame buildings with diaphragms under seismic actions (Part 2) - Rules of formation. “SEISAN-KENKYU�Monthly Journal of Institute of Industrial Science, University of Tokyo (1991)4, Vol.43:28-31. Melkumyan, M. First application of the dynamic damper in the design of seismically isolated dwelling house. Proceedings of the Third European Conference on Structural Control, Vienna, Austria (2004), Vol. I:M6-9 - M6-12.
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