Optimum Dynamic Characteristic Control Approach for Building Mass Damper Design

Transcription

1 Optimum Dynamic Characteristic Control Approach or Building Mass Damper Design S.J. Wang, B.H. Lee & Y.W. Chang National Center or Research on Earthquake Engineering, Taipei, Taiwan. K.C. Chang & C.H. Yu Department o Civil Engineering, National Taiwan University, Taipei, Taiwan. 017 NZSEE Conerence J.S. Hwang Department o Civil and Construction Engineering, National Taiwan University o Science and Technology, Taipei, Taiwan. ABSTRACT: A new seismic design manner, namely building mass damper (BMD), which comes rom a combination o mid-story isolation and tuned mass damper (TMD) design concepts, recently attracts immense attention. In this study, an imum building mass damper (OBMD) design approach, namely imum dynamic characteristic control approach, is proposed to seismically protect both the superstructure (or tuned mass) and the substructure (or primary structure) respectively above and below the control layer. A series o sensitivity analyses and experimental studies on dierent parameters, including mass, requency, and damping ratios, o a building designed with a BMD system were conducted. The test results veriy the practical easibility o the BMD concept as well as the eectiveness o the proposed OBMD design. 1 INTRODUCTION The mid-story isolation design is recently gaining popularity owing to its advantages in terms o construction eiciency, space use, and maintenance over the conventional base isolation design. Previous researches have investigated the seismic responses o mid-story isolated buildings (Wang et al. 01; Wang et al. 01). It was indicated that the mid-story isolation design is eective in reducing the seismic demand o the superstructure above the isolation system i the coupling o higher modes is precluded. However, due to the lexibility o the substructure and the contribution o higher modes, the seismic response o the substructure below the isolation system may be enlarged. Tuned mass dampers (TMDs) have been recognized as an eective passive energy absorbing device to reduce the undesirable oscillation o the attached vibrating system (or primary system) subjected to harmonic excitation (Den Hartog 1956; Lut 1979). arious approaches or selecting the imum design parameters o such a system have been developed. For instance, to minimize the steady-state response o the primary system, Den Hartog (1956) derived the close-orm solutions or the imum tuning requency and damping ratio o a TMD system attached to an undamped system under harmonic excitation. Ater that, Warburton (198) studied the imum TMD design parameters or an undamped system subjected to harmonic external orce and white-noise random excitation. However, all systems contain some damping in reality. Tsai and Lin (199) studied the imum TMD design parameters or a damped system by numerical iteration and curve-itting procedures. Sadek s criterion (1997) or seismic application was to select, or a given mass ratio, the tuning requency and damping ratio that would result in equally large modal damping in the irst two modes o vibration. The TMD design concept was irst aded to mitigate the wind-induced vibration or enhance the serviceability o high-rise buildings, and was subsequently aded to enhance the seismic capability o building structures. Until now, the eectiveness o the TMD design in reducing structural responses subjected to seismic loading is still arguable (Sladek & Klingner 198), especially when the tuned mass is much smaller than the primary structure. To overcome the concern o limited response reduction due to insuicient tuned mass in the conventional TMD design, a new design concept,

2 namely building mass damper (BMD), was proposed and numerically studied in some researches. In the BMD system, as implied in the name, a part o structural mass, instead o additional mass, is intended to be an energy absorber. Ziyzeiar and Noguchi (1998) utilized an isolation layer composed o elastic bearings and viscous dampers to isolate a part o the structure in a tall building or versatile design goals. One o the goals was to reduce the seismic response o the substructure below the isolation layer by means o signiicant and out-o-phase movement o the isolated superstructure as a vibration absorber. In addition, based on the numerical results o a 1-story building subjected to various seismic excitations, illaverde (00) indicated that the insertion o lexible laminated rubber bearings and viscous dampers between the roo and the rest o the building, namely roo isolation system, can eectively reduce the seismic response o the building. That is, the roo isolation system was designed to be a vibration absorber. The BMD concept has been applied to a ew new constructions and retroitted buildings; or instance, the Swatch Group Japan Headquarter in Tokyo and the Theme Building at the Los Angeles International Airport. However, among these applications, the control target was still ocused on the substructure (or primary structure) perormance rather than on either the superstructure (or tuned mass) perormance or both. I the superstructure in the BMD design is intended to be used or occupancy as the substructure, excessive dynamic responses are not acceptable deinitely. Under this circumstance, the seismic perormance o both the substructure and superstructure should be paid attention. In this study, to combine the advantages o seismic isolation and TMD designs, an imum design method or a BMD system is investigated. A building structure designed with a BMD system is rationally assumed to be represented by a simpliied three-lumped-mass structure model. Reerring to Sadek s research (1997), the objective unction is reined as that the three modal damping ratios obtained rom the simpliied structure model in the direction o interest are equally important and taken as an approximately equal value. Accordingly, the imum building mass damper (OBMD) design parameters can be rationally determined based on the proposed imum dynamic characteristic control approach. First, the inluences o varied mass ratios and inherent damping ratios on the OBMD design parameters are quantitatively discussed. Then, a series o shaking table tests were perormed to veriy the easibility o the BMD concept as well as the eectiveness o the proposed OBMD design on seismic protection o the building models. ANALYTICAL STUDY.1 Simpliied three-lumped-mass structure model In this study, the BMD system is intended to be installed upon a multi-story substructure (or primary structure). The system is essentially composed o a multi-story superstructure (or tuned mass) as well as spring and dashpot elements or connecting the superstructure to the substructure. The stiness and damping designed or the BMD system, o course, are provided by the spring and dashpot elements, respectively. A simpliied three-lumped-mass structure model, in which the three lumped mass are respectively assigned at the superstructure (SUP), control layer (CL), and substructure (SUB), is rationally assumed to represent a building structure designed with a BMD system, as shown in Figure 1. For doing so, an excessive (or unreasonable) damping demand or the OBMD design owing to a signiicant superstructure-to-substructure mass ratio and neglect o lexibility o the superstructure can be precluded, which will be urther discussed in Section.. The equation o motion or the simpliied structure model in the horizontal direction can be written as Mu Cu Ku MR u g m1 0 0 u1 c1 c c 0 u1 0 m 0 u c c c c u 0 0 m u 0 c c u k1 k k 0 u1 m k k k k u 0 m k k u m u g (1)

3 where M = the generalized seismic reactive mass matrix; m 1, m, and m = the generalized seismic reactive masses or the undamental mode o vibration computed or a unit modal participation actor o the substructure, control layer, and superstructure, respectively ; K and C = the horizontal generalized stiness and damping coeicient matrices, respectively; k 1 (c 1), k (c ), and k (c ) = the horizontal stiness (viscous damping coeicients) or the undamental mode o vibration o the substructure, control layer, and superstructure, respectively; u = the horizontal displacement vector relative to ground; u 1, u, and u = the horizontal displacements o the substructure, control layer, and superstructure relative to ground, respectively; = the horizontal ground acceleration; and R = the u g earthquake inluence vector. The equation o motion given in Equation (1) can also be expressed in terms o the nominal requency ω 1, requency (or tuning) ratio i i (i =, ), mass ratio 1 i m i m 1 (i =, ), and component damping ratio i ci ji m (i = 1~), in which i and j = 1,, and denote the substructure, control layer, and superstructure, respectively; and the nominal requencies ω 1, ω, and ω are deined as k / ( m m ), and, respectively. k / m 1 1, j i k / m Figure 1. Simpliied three-lumped-mass structure model or BMD design.. Optimum design method based on modal characteristic control concept By means o the state space method under coupling approximation, the system matrix A or Equation (1) can be obtained. Accordingly, the complex eigenvalues can be calculated in a orm o conjugate pairs. The proposed objective unction to determine the OBMD design parameters in this study is modiied rom Sadek s research (1997). Three modal damping ratios which are dominant respectively or response mitigation o the substructure, control layer, and superstructure in the direction o interest ' ' ' are equally important and are taken as an approximately equal value, i.e. ξ1 ξ ξ. Based on the proposed objective unction with given ω 1, μ, μ, ξ 1, and ξ, the imum design parameters or,, and ξ, i.e.,, and, respectively, can be determined. ξ. Sensitivity analysis considering varied mass and damping ratios Assume that the mass ratios μ and μ vary within a reasonable range respectively rom 0.1 (i.e. basically representing a high-rise substructure) to 0.5 (i.e. basically representing a low-rise substructure) and 0.1 (i.e. basically representing a low-rise superstructure) to (i.e. the story number o the superstructure is twice as many as that o the substructure). Besides, assume that both ξ 1 and ξ are set to be % and 10% to correspondingly represent a bare structure and a structure with additional damping devices. Thereore, on the basis o the proposed objective unction, the imum damping ratio ξ and the imum requency (or tuning) ratios and or the OBMD design varying with dierent μ, μ, ξ 1, and ξ are calculated and shown in Figure. It can be seen that ξ,, and, in general, are proportional to μ and are inversely proportional to μ. This trend is less signiicant when μ and μ become larger gradually. It is implied that a decrease o μ and an increase o μ may reduce the OBMD design demands. In addition, ξ will increase when ξ 1 is increased and will decrease when ξ is increased. Increasing ξ will lead to an increased demand o while will

4 reduce the demand o. On the other hand, the variation o the imum requency ratios with dierent ξ 1 is very sensitive to the mass ratios. When ξ 1 is increased, the demand o will generally decrease except or the nearly same trend at μ equal to 0.1, and the demand o will decrease i μ is small and will increase slightly with larger μ. In Sadek s study (1997) and many past researches relevant to the TMD design, a simpliied twolumped-mass structure model was usually utilized to study the imum TMD design parameters. Under this circumstance, only one mass ratio, i.e. a total o μ and μ, was required to be deined. It was rarely concerned whether the damping demand is reasonable and practicable i the mass ratio becomes larger. As shown in Figure, the dotted line represents the trend o the imum damping ratio varying with respect to the mass ratio obtained rom Sadek s research (the inherent damping ratio is assumed to be %). It is ound that the imum damping ratio is proportional to the mass ratio, i.e. the larger the mass ratio, the higher the damping demand required. The solid lines represent the variation o the imum damping ratio with dierent combinations o μ and μ when using the simpliied three-lumped-mass structure model and the proposed imum dynamic characteristic control approach (ξ 1=ξ =%). Apparently, an opposite tendency that the imum damping ratio, in general, is inversely proportional to the total o μ and μ but proportional to μ is observed. More importantly, a more reasonable and applicable damping demand can be obtained especially when μ becomes smaller. Figure. Optimum damping and requency ratios with respect to μ, μ, ξ1, and ξ. Figure. Optimum damping ratio obtained in Sadek s study (1997) and this study. 4

5 SEISMIC SIMULATION TESTS.1 Test structure models The bare specimen was designed to be a 1/4 scaled 8-story steel structure model with single-bay widths o 1.5m and 1.1m respectively in the X and Y directions, as shown in Figure 4(a). Each loor was 1.1m high and each slab was 0mm thick. The columns and beams were wide lange with a sectional dimension o (mm) and channel with a sectional dimension o (mm), respectively. Additional live load o 0.5kN-sec /m simulated by mass blocks with a regular plane arrangement was assigned at each loor. Apart rom the bare specimen, the BMD specimens were designed with a control layer (CL) at the ourth loor, as shown in Figure 4(b). In other words, the substructure (or primary structure) and superstructure (or tuned mass) were three- and our-story structure models, respectively. In this study, or simplicity and practical easibility, elastomeric bearings (RBs) with a diameter o 180mm and linear luid viscous dampers (FDs) were rationally aded to play the roles o spring and dashpot elements at the control layer, respectively. A series o BMD specimens, i.e. BMD-1 to BMD-7 as given in Table 1, were designed to urther discuss the inluence o varying design parameters on their seismic perormance. BMD-, BMD-1, and BMD-, the irst-group specimens, were intended to only have dierent values in ascending order but the other design parameters remained the same. BMD- 4, BMD-1, and BMD-5, the second-group specimens, were intended to only have dierent values in ascending order. BMD-6, BMD-1, and BMD-7, the third-group specimens, were intended to only have dierent ξ values in ascending order. The modal characteristics o the 8-story bare specimen, three-story substructure, and our-story superstructure were experimentally identiied under white noise excitation. Ater obtaining the realistic characteristics, the imum design parameters,, and or the OBMD specimen as shown in Figure 4(c) can be designed according to the proposed objective unction with known ω 1, μ, μ, ξ 1, and ξ, as detailed in Table 1. Specimen ξ Table 1. Design parameters or all test and numerical structure models. Total stiness at CL (4 sets o RBs) Total rubber thickness o RBs ξ Total damping coeicient at CL ( sets o FDs) Sectional dimension o added braces at substructure (SUB) (%) (kn/m) (mm) (kn-sec/m) (mm) BMD L (SUB) BMD L (SUB) BMD L (SUB) BMD L (SUB) BMD L (SUB) BMD L (SUB) BMD L (SUB) OBMD L (SUB) (a) Bare specimen (b) BMD specimen (c) OBMD specimen Figure 4. Experimental structure models. 5

6 . Input ground motions Four recorded ground motions, denoted as El Centro, Kobe, TCU047, and THU thereater, with various peak ground acceleration (PGA) levels were selected or the earthquake inputs o the uniaxial shaking table tests (i.e. along the X direction o the specimens), as summarized in Table. Since the specimens were assumed as a 1/4 scaled structure model, a time scale o 1/ 4 was considered or the earthquake inputs to meet the similitude law. Note that the maximum test PGA level was determined on the premise o the specimens remaining essentially elastic. Table. Earthquake test program. Test name El Centro Kobe TCU047 THU Earthquake record El Centro/I-ELC70 Imperial alley, USA 1940/05/19 KJMA/KJM000 Kobe, Japan 1995/01/16 Chi-Chi/TCU047 Chi-Chi, Taiwan 1999/09/1 Tohoku/THU Tohoku, Japan 011/0/11 Original PGA 0.5g 0.8g 0.40g 0.g Test PGA Original PGA 80% 160% 40% 40% 60% 80% 80% 160% 40% 50% 100% 150% Bare specimen. Inluence o varying design parameters on seismic perormance BMD OBMD The maximum-acceleration ratio (AR 1) and maximum-inter-story-displacement ratio (IDR 1) o BMD-, BMD-, BMD-4, BMD-5, BMD-6, and BMD-7 to BMD-1, as calculated respectively in Equations () and (), at dierent loors excluding the control layer (or 4F) are shown in Figure 5. AR Max Acc Max Acc () 1 BMDi, j BMD1, j IDR Max ID Max ID () 1 BMDi, j BMD1, j where the subscript i = ~7 represent BMD- to BMD-7; the subscript j represents the j th loor (j = 1~8); Max Acc BMD-i, j and Max ID BMD-i, j represent the maximum acceleration and inter-story displacement responses at the j th loor o BMD-i (i = ~7), respectively; Max Acc BMD-1, j and Max ID BMD-1, j represent the maximum acceleration and inter-story displacement responses at the j th loor o BMD-1, respectively. As observed rom these igures, in general, decreasing may cause enlarged acceleration responses at the substructure, while increasing may result in enlarged ones at both the substructure and superstructure, particularly or lower stories o the substructure and upper stories o the superstructure. Decreasing may cause enlarged inter-story-displacement responses at the superstructure, while increasing may result in enlarged ones at the substructure. Increasing may enlarge the acceleration responses o the substructure. Neither decreasing nor increasing causes signiicantly enlarged interstory-displacement responses at the substructure and superstructure. It is o no surprise that the acceleration responses at both the substructure and superstructure o BMD-6 are larger than those o BMD-1 because o its smaller ξ. However, when ξ becomes very large, e.g. ξ =5% in BMD-7, it may not be very helpul and even slightly harmul to the acceleration control perormance compared to BMD-1 (ξ =%). The inluence o varying ξ on the inter-story-displacement control at the substructure is more signiicant than that at the superstructure. Among BMD-1 to BMD-7 under all the earthquake excitation, the maximum inter-story displacement response at the control layer is 0.5mm, which is corresponding to a shear strain o 75.9% or RBs. 6

7 Figure 5. AR1 and IDR1 o BMD-, BMD-, BMD-4, BMD-5, BMD-6, and BMD-7 to BMD-1..4 Comparison o seismic responses between bare, BMD, and OBMD specimens The vertical distributions o maximum acceleration and inter-story displacement responses o the bare and OBMD specimens under 50% THU are presented in Figure 6, respectively. To statistically and overall demonstrate that the OBMD specimen designed based on the proposed objective unction can have a superior seismic perormance to the bare and BMD specimens, the average maximumacceleration ratio (AR ) and average maximum-inter-story-displacement ratio (IDR ) o the bare and BMD specimens to the OBMD specimen, as calculated respectively in Equations (4) and (5), at the three-story substructure and our-story superstructure are shown in Figure 7. AR Max Acc (or Max Acc ) Max Acc (4) BMDi, j Bare, j OBMD, j IDR Max ID (or Max ID ) Max ID (5) BMDi, j Bare, j OBMD, j where the subscript i = 1~7 represent BMD-1 to BMD-7; Max Acc BMD-i, j, Max Acc Bare, j, and Max Acc OBMD, j represent the maximum acceleration responses at the j th loor o BMD-i (i = 1~7), the bare specimen, and the OBMD specimen, respectively; Max ID BMD-i, j, Max ID Bare, j, and Max Acc OBMD, j represent the maximum inter-story displacement responses at the j th loor o BMD-i (i = 1~7), the bare specimen, and the OBMD specimen, respectively. Note that when the ratio is larger than unity and becomes higher, a better control perormance o the OBMD specimen can be achieved. As observed rom these igures, the seismic perormance o the OBMD specimen is much better than that o the bare specimen. In addition, the OBMD specimen has a superior potential in reducing the seismic responses to the BMD specimens, especially or the acceleration control perormance at the superstructure as well as the inter-story displacement control perormance at both the substructure and superstructure. It is experimentally demonstrated that the proposed imum dynamic characteristic control approach or the OBMD design is eective and necessary. Under all the earthquake excitation as listed in Table, the maximum inter-story displacement response at the control layer o the OBMD specimen is 1.mm, which is corresponding to a shear strain o 64.% or RBs. Figure 6. ertical distributions o maximum responses o bare and OBMD specimens under 50% THU. 7

8 Figure 7. Average AR and IDR o bare and BMD specimens to OBMD specimen at SUB and SUP. 4 CONCLUSIONS The objective unction to determine the OBMD design parameters in this study is modiied rom Sadek s research (1997) and derived based on a simpliied three-lumped-mass structure model. The sensitivity analysis results show a dierent trend or the imum damping ratio varying with respect to the mass ratio rom Sadek s study and many other past researches, i.e. the larger the mass ratio, the lower the damping demand required. Thus, by using the proposed imum dynamic characteristic control approach to design a building with a BMD system, a reasonable and applicable damping demand can be obtained. The shaking table test results indicate that varying design parameters will cause entirely dierent seismic perormances o a building with a BMD system. On the whole, moderately smaller and as well as larger ξ can have a better control perormance. Undeniably, however, the seismic perormance o the BMD design, like the conventional TMD design, is strongly related to the requency content o the seismic excitation. In addition, the proposed OBMD design has a superior potential in reducing the seismic responses o both the substructure and superstructure to the BMD design, which demonstrates the eectiveness and signiicance o the proposed imum dynamic characteristic control approach. Undoubtedly, the seismic perormance o the proposed OBMD design is much better than a counterpart without any structural control technology. 5 REFERENCES Den Hartog, J.P. (4th edn). (1956). Mechanical ibrations, NY: McGraw-Hill. Lut, R.W. (1979). Optimum tuned mass dampers or buildings. Journal o the Structural Division, ol 105: Sadek, F., Mohraz, B., Taylor, A.W. & Chung, R.M. (1997). A method o estimating the parameters o tuned mass dampers or seismic applications. Earthquake Engineering and Structural Dynamics, ol 6(6): Sladek, J.R. & Klingner, R.E. (198). Eect o tuned-mass dampers on seismic response. Journal o Structural Engineering, ASCE, ol 109(8): Tsai, H.C. & Lin, G.C. (199). Optimum tuned-mass dampers or minimizing steady-state response o supportexcited and damped systems. Earthquake Engineering and Structural Dynamics, ol (11): illaverde, R. (00). Aseismic roo isolation system: easibility study with 1-story building. Journal o Structural Engineering, ASCE, ol 18(): Wang, S.J., Changm K.C., Hwang, J.S., Hsiao, J.Y., Lee, B.H. & Hung, Y.C. (01). Dynamic behavior o a building structure tested with base and mid-story isolation systems. Engineering Structures, ol 4: Wang, S.J., Hwang, J.S., Chang, K.C., Lin, M.H. & Lee, B.H. (01). Analytical and experimental studies on mid-story isolated buildings with modal coupling eect. Earthquake Engineering and Structural Dynamics, ol 4(): Warburton, G.B. (198). Optimal absorber parameters or various combinations o response and excitation parameters. Earthquake Engineering and Structural Dynamics, ol 10(): Ziyaeiar, M. & Noguchi, H. (1998). Partial mass isolation in tall buildings. Earthquake Engineering and Structural Dynamics, ol 7(1):