36 2010 8 8 Vol 36 No 8 JOURNAL OF BEIJING UNIVERSITY OF TECHNOLOGY Aug 2010 Ⅰ 100124 TB 534 + 2TP 273 A 0254-0037201008 - 1091-08 20 Hz 2 ~ 8 Hz 1988 Blondet 1 Trombetti 2-4 Symans 5 2 2 1 1 1b 6 M p s 2 x p + C p sx p + K p x p = - M p s 2 x t M p C p K p x p x t x p x t = - M p s 2 1 M p s 2 + C p s + K p 2 1a x tp = x t + x p 2 x tp x t s= C p s + K p M p s 2 + C p s + K p = s 2 2ζ p ω p s + ω 2 p + 2ζ p ω p s + ω 2 p F ts = - M p s 2 x tp = - M p ss 2 x t 1c 3 4 2009-10-12 9071501090715032 bcx -2009-033 1962
1092 2010 1 Fig 1 Shaking table with SDOF payload M t + M p s s 2 x t + C t sx t + K t x t = F act M t C t K t F act M es M es = M t + M p s 5 6 6 7 4βA p k q0 H s s= M es Vs 3 + 4βC c + C t V s 2 + 4βA 2 p + VK t + 4βC c C t s + 4βC c K t 8 3 m 3 m 6 t 5 Hz 0 05 2 3 2 7 8 7 2 Fig 2 Frequency response of shaking table physical system under different payloads 3 ~ 5 2 5 8 Hz 0 05 6 5 Hz 0 02 3 ~ 5
8 Ⅰ 1093 4 6 3 ~ 6 3 Hz 10 Hz 15 3 Fig 3 ω p = 2 Hz ξ p = 0 05 Frequency response of shaking table with SDOF payload based on rigid mass control parameterω p = 2 Hz ξ p = 0 05 4 Fig 4 ω p = 5 Hz ξ p = 0 05 Frequency response of shaking table with SDOF payload based on rigid mass control parameterω p = 5 Hz ξ p = 0 05 5 Fig 5 ω p = 8 Hz ξ p = 0 05 Frequency response of shaking table with SDOF payload based on rigid mass control parameterω p = 8 Hz ξ p = 0 05
1094 2010 6 Fig 6 ω p = 5Hz ξ p = 0 02 Frequency response of shaking table with SDOF payload based on rigid mass control parameterω p = 5 Hz ξ p = 0 02 6 6 s 1 7 s 3 Hz 10% 3 Hz 50 Hz 7 Fig 7 s Frequency response of s 2 8 m p s 2 x p + c p sx p + k p x p = - m p s 2 x t x p = - N n = 1 φ T n m p I s 2 φ n M n s 2 + 2ζ n ω n s + ω 2 n 8 x tp = x p + Ix t 9 x tpn x t x t 8 9
8 Ⅰ 1095 H pm s= x tp x t = I - N n = 1 φ n m p I s 2 φ n M n s 2 + 2ζ n ω n s + ω 2 n 10 8~ 10 m p c p k p I = 1 1 T x p = x p1 x p2 x pn T x t φ n = φ n1 φ n2 φ nn T n M n ω n ζ n n = x tp1 x tp2 x tpn T F tm = - s 2 N n = 1 x tp m n x tpn = - s 2 x t m p I T H pm s 1 11 M em = M t + m p I T H pm s 4βA p k q0 H m s= M em Vs 3 + 4βC c + C t V s 2 + 4βA 2 p + VK t + 4βC c C t s + 4βC c K t 13 8 m 1 = m 2 = m 3 = 1 tk 1 = k 2 = k 3 = 625 kn / mω 1 = 1 77 Hz ω 2 = 4 96 Hz ω 3 = 7 17 Hz ξ 1 = ξ 2 = ξ 3 = 0 01 ω k = ω 1 ω 2 ω 3 ξ k = ξ 1 ξ 2 ξ 3 9 ~ 11 1 3 5 5 8 12 Fig 8 Shaking table with MDOF payload 3 2 9 ~ 12 11 12 13 9 Fig 9 ω = ω k ξ = 5ξ k Frequency response of shaking table with MDOF payload based on rigid mass control parameterω = ω k ξ = 5ξ k
1096 2010 10 Fig 10 ω = 3ω k ξ = 5ξ k Frequency response of shaking table with MDOF payload based on rigid mass control parameterω = 3ω k ξ = 5ξ k 11 Fig 11 ω = 5ω k ξ = 5ξ k Frequency response of shaking table with MDOF payload based on rigid mass control parameterω = 5ω k ξ = 5ξ k 12 Fig 12 ω = 3ω k ξ = 2ξ k Frequency response of shaking table with MDOF payload based on rigid mass control parameterω = 3ω k ξ = 2ξ k 13 H pm s
8 Ⅰ 1097 13 Fig 13 H pm s Frequency response of H pm s 3 2 1 5 2 Elcentro NS 1 /10 14 15 14 Elcentro NS 15 Elcentro NS Fig 14 Time history of Elcentro NS wave under rigid mass Fig 15 Time history of Elcentro NS waveunder un-loaded condition 4 3 Hz 1BLONDET MESPARZA C Analysis of shaking table-structure interaction effects during seismic simulation testsj Earthquake Engineering & Structural Dynamics198816473-490 2TROMBETTI T L Analytical modeling of a shaking table systemd HoustonDepartment of Civil EngineeringRice University199729-129 3CONTE J PTROMBETTI T L Linear dynamic modeling of a uni-axial servo-hydraulic shaking table systemj Earthquake Engineering & Structural Dynamics2000299 1375-1404
1098 2010 4TROMBETTI T LCONTE J P Shaking table dynamicsresults from a test-analysis comparison studyj Journal of Earthquake Engineering200264 513-551 5SYMANS MTWITCHELL B System identification of a uniaxial seismic simulatorc Proc 12th Engineering Mechanics Conference RestonVAAmerican Society of Civil Engineers1998758-761 6CHOPRA A K Dynamic of structuresm CaliforniaPrentice Hall199515-32 7 H E M 1976199-246 8 M 200859-76 Effects on the Earthquake Simulation Caused by the Characteristics of the Specimen in the Shaking Table Tests-Part 1 Effects on the Stability of the System LI Zhen-baoTANG Zhen-yunZHOU Da-xingJI Jin-baoMA Hua Beijing Key Lab of Earthquake Engineering and Structural RetrofitBeijing University of TechnologyBeijing 100124China AbstractThe specimen is assumed to be a rigid mass in the design of the shaking table control system but in factthere is a big difference between the specimen and the shaking table system caused by the assumption of the rigid mass of the specimen This results in the control system operating in a narrow frequency band and poor stability reducing the replaying precision of the recorded seismic waves In this papermodels are established both for the SDOF and MDOF systems which are designed to be the rigid mass and non-rigid massand then through the analysis of these modelsthe performances of the control systems are evaluated The conclusion is that the stability of the system designed for the non-rigid mass performs best in the unloaded condition and the stability of shaking table is greatly improved Key wordsshaking tablerigid payloadnon-rigid payloadcontrol parameter