2 ~ 8 Hz Hz. Blondet 1 Trombetti 2-4 Symans 5. = - M p. M p. s 2 x p. s 2 x t x t. + C p. sx p. + K p. x p. C p. s 2. x tp x t.

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Download "2 ~ 8 Hz Hz. Blondet 1 Trombetti 2-4 Symans 5. = - M p. M p. s 2 x p. s 2 x t x t. + C p. sx p. + K p. x p. C p. s 2. x tp x t."

Ἀριστόβουλος Δουρέντης
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1 Vol 36 No 8 JOURNAL OF BEIJING UNIVERSITY OF TECHNOLOGY Aug 2010 Ⅰ TB TP 273 A Hz 2 ~ 8 Hz 1988 Blondet 1 Trombetti 2-4 Symans b 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 bcx

2 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 βA 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 Fig 2 Frequency response of shaking table physical system under different payloads 3 ~ Hz Hz ~ 5

3 8 Ⅰ ~ 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 = 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 = 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

4 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 = 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

5 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 ~ Fig 8 Shaking table with MDOF payload ~ 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

6 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

7 8 Ⅰ Fig 13 H pm s Frequency response of H pm s Elcentro NS 1 / 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 Dynamics TROMBETTI T L Analytical modeling of a shaking table systemd HoustonDepartment of Civil EngineeringRice University CONTE J PTROMBETTI T L Linear dynamic modeling of a uni-axial servo-hydraulic shaking table systemj Earthquake Engineering & Structural Dynamics

8 TROMBETTI T LCONTE J P Shaking table dynamicsresults from a test-analysis comparison studyj Journal of Earthquake Engineering SYMANS MTWITCHELL B System identification of a uniaxial seismic simulatorc Proc 12th Engineering Mechanics Conference RestonVAAmerican Society of Civil Engineers CHOPRA A K Dynamic of structuresm CaliforniaPrentice Hall H E M M 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 China 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

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