NONLINEAR DYNAMIC ANALYSIS OF STRUCTURES WITH VISCOUS DAMPERS

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1 21 1 Vol.21 No ENGINEERING MECHANICS Feb (2004) ( ) HBTA HBTA TU352.1 A NONLINEAR DYNAMIC ANALYSIS OF STRUCTURES WITH VISCOUS DAMPERS TANG Yu-chuan, ZHANG Yu-liang, ZHANG Tong-sheng (Department of Civil Engineering, Tsinghua University, Beijing , China) Abstract: Based on the story model of spatial member, the supplemental damping matrix, dynamic balance equation and relative energy balance equation of structures with viscous dampers are derived. Nonlinear dynamic analysis of structures with viscous dampers is added into the computer program HBTA (highrise building time-history analysis). Examples are provided to validate the dynamic analysis method and observe the seismic mitigation effect of viscous dampers. The inner forces and deformation of structural members and viscous dampers can be given by HBTA. Efforts are made to conduct dynamic analysis including both displacement-dependent nonlinearity and velocity-dependent nonlinearity. Key words: structure with energy dissipation system; viscous damper; dynamic analysis; energy analysis 1 SAP2000 CANNY [1] [2] (GB ) (1977) (1945) ( zhangyl@tsinghua.edu.cn) (1934)

2 68 C i C i ( x, y ) i (2) 1 xyz 1 (3) l xx x x (4) ( x 2, y 2 ) 2 (1) [3] C C ( x j, y j ) j (2) 2 x HBTA [4] (5) (3) (4) (5) (1) 2 xyz x 2.1 (6) xyz ui v i θ i u j v j θ j 1 (7) Fig.1 Coordinate systems m τ = kγ& { F DP } τ γ& k m k m (8) [5] F [M] [C] x& Rayleigh [K] (1) c m =1 {d} m 1 Taylor { F g } (8) i [ u & T i v& i θ & (9) i ] ui v i θ i [C] [K] i x y z (8) (9) 1 1 xyz (2) ) ( x1, y

3 69 (i) (i) (i) (i) i (7) i (10) (16) [6] (11) (16) [ C ] e DP [ C DP ] HBTA (12) (12) (9) [5] (13) [C] [K] 1.32m 1.32m m [ C DP ] m cm cm 2 1~4 578kg 5 596kg Wilson-θ X (13) c=10kn s/m m=0.6 Wilson-θ 3.2 [2] X El Centro NS Wilson-θ 341.7gal X 0.25s s 0.01s HBTA HBTA SAP2000 (8) X 2 X T T D ({ d( τ )} ) = { d& ( τ )} dτ 3 HBTA SAP2000 X 4(a) (14) X 4(b) ( { F ( τ )} = HBTA ) { F ( τ )} = [ t i, t i + 1 D R (14) Fig.2 Displacement response of top story ] (15) E K E D E R E DP 3 HBTA [7] 2 3

4 70 HBTA % HBTA 8 [6] 92m X 3 ( 8.6m) Y 4 ( 8.6m 10.0m) H HBTA Q345B 4.30kN/m 2 1~9 6.00kN/m ~ (15) II Taft SE NE 6 SAP2000 II HBTA 6 SAP HBTA (GB ) (a) (b) 4 Fig.4 Maximum response of each story 5 6 Fig.5 Damping force versus relative displacement in damper Fig.6 Time-history trace of energy dissipated by dampers HBTA SAP Taft 3 ( : kn s/m) Table 3 Damping coefficients of dampers (Unit: kn s/m) HBTA 4 X 400gal Y 340gal 20s 0.02s 2~16 1/70 (JGJ99-98) [8] X Y 1~20 X Y 8 1~2 3~14 15~18 19~20 X Y HBTA 1/ M 8 x Fig.7 Maximum displacement angle between stories Fig.8 Moment response at the top of column

5 Fig.9 Time-history trace of energy in original structure 5 Fig.10 Time-history trace of energy in damped structure HBTA HBTA SAP2000 HBTA ( 158 )

6 158 Stadium [A]. Proceedings of the Fifth International (1) Conference on Wind Engingeering, Colorado State m ac = Uρ l University, Pergamon Press [3] Sewall J L, Miserentino R, Papppa R S. Vibration studies P of a lightweight three-sided membrane suitable for space k k application[m]. NASA Technical Paper 2095, P 0.515~0.596 [4] R Sygulski. Dynamic analysis of open membrane structures interaction with air[j]. International Journal for (2) Numerical Method in Engineering, 1994,37: [5]. [J]. m a 0 = Uρ l U, 2001,11: t ω H / l Yang Qinshan. The function of dynamic coupling between ω t 0 π / 2 U the tensile membrane structures and wind conditions[j] l H / Proceedings of the Tenth National Conference on Wind U Engineering, 2001,11: (in Chinese) [J]., [1],. [M]., Tong Binggang. The movement of uncertain flow and vortex[a]. Beijing: National Defense Industrial Press, (in Chinese) [2] Irwin H P A H, Wardlaw R L. A wind tunnel invetigation of the retractable fabric roof for the Montreal Olympic ( 71 ) [6],. 2001, 11: Shen Shizhao. Wu Yue. The progress on investigation of dynamic response of wind-induced tensile structures[j]. Proceedings of the Tenth National Conference on Wind Engineering. 2001,11: (in Chinese) [1],,. Lu Jing, Zhang Tongsheng, Cui Hongchao. Elasto-plastic : [J]., time-history analysis for Yuanyang Plaza in Dalian [J]. 2001, 21(4): Ou Jinping, Wu Bin, et al. Analysis and design of seismic retrofit of Beijing Hotel with energy dissipators: time history method [J]. Earthquake Engineering and Engineering Vibrations, 2001, 21(4): (in Chinese) [2],,. 1994, 16(6): [J]. ( [7] K C Chang, M L Lai, T T Soong, et al. Seismic behavior ), 2001, 31(1): Yang Guohua, Li Aiqun, et al. Analysis of controlling vibration response of viscous fluid damper for engineering structures[j]. Journal of Southeast University (Natural Science Edition), 2001, 31(1): (in Chinese) [3],,. Wu Wenjie. Researches on design theory of MDOF [J]., 1980, (1): Sun Yeyang, Yu Andong, et al. Elasto-plastic dynamic analysis for tall buildings with member-story model [J]. Journal of Tongji University, 1980,(1):87-97.(in Chinese) [4],,. [J]., 1998, 28(10): Building Structures, 1998, 28(10): (in Chinese) [5] Gary C Hart, Kevin Wong. Structural dynamics for structural engineers[m]. Wiley, [6] Andr Filiatrault, et al. On the computation of seismic energy in inelastic structures[j]. Engineering Structures, and design guidelines for steel frame structures with added viscoelastic dampers[r]. Tech. Rep. NCEER , SUNY at Buffalo, [8]. MDOF [D]., structures with viscous passive energy dissipation based on energy criteria[d]. Beijing: Tsinghua University, (in Chinese)

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