This thesis presents an Experimental/Analytical approach to modeling and calibrating shaking tables for structural dynamic applications. This approach was successfully applied to the shaking table recently built in the structural laboratory of the Civil Engineering Department at Rice University.
This shaking table is capable of reproducing model earthquake ground motions with a peak acceleration of 6 g's, a peak velocity of 40 inches per second, and a peak displacement of 3 inches, for a maximum payload of 1500 pounds. It has a frequency bandwidth of approximately 70 Hz and is designed to test structural specimens up to 1/5 scale. The rail/table system is mounted on a reaction mass of about 70,000 pounds consisting of three 12 ft x 12 ft x 1 ft reinforced concrete slabs, post-tensioned together and connected to the strong laboratory floor. The slip table is driven by a hydraulic actuator governed by a 407 MTS controller which employs a proportional-integral-derivative-feedforward-differential pressure algorithm to control the actuator displacement. Feedback signals are provided by two LVDT's (monitoring the slip table relative displacement and the servovalve main stage spool position) and by one differential pressure transducer (monitoring the actuator force).
The dynamic actuator-foundation-specimen system is modeled and analyzed by combining linear control theory and linear structural dynamics. The analytical model developed accounts for the effects of actuator oil compressibility, oil leakage in the actuator, time delay in the response of the servovalve spool to a given electrical signal, foundation flexibility, and dynamic characteristics of multi-degree-of-freedom specimens.
In order to study the actual dynamic behavior of the shaking table, the transfer function between target and actual table accelerations were identified using experimental results and spectral estimation techniques. The power spectral density of the system input and the cross power spectral density of the table input and output were estimated using the Bartlett's spectral estimation method.
The experimentally-estimated table acceleration transfer functions obtained for different working conditions are correlated with their analytical counterparts. As a result of this comprehensive correlation study, a thorough understanding of the shaking table dynamics and its sensitivities to control and payload parameters is obtained. Moreover, the correlation study leads to a calibrated analytical model of the shaking table of high predictive ability. It is concluded that, in its present conditions, the Rice shaking table is able to reproduce, with a high degree of accuracy, model earthquake accelerations time histories in the frequency bandwidth from 0 to 75 Hz. Furthermore, the exhaustive analysis performed indicates that the table transfer function is not significantly affected by the presence of a large (in terms of weight) payload with a fundamental frequency up to 20 Hz. Payloads having a higher fundamental frequency do affect significantly the shaking table performance and require a modification of the table control gain setting that can be easily obtained using the predictive analytical model of the shaking table.
The complete description of a structural dynamic experiment performed using the Rice shaking table facility is also reported herein. The object of this experimentation was twofold: (1) to verify the testing capability of the shaking table and, (2) to experimentally validate a simplified theory developed by the author, which predicts the maximum rotational response developed by seismic isolated building structures characterized by non-coincident centers of mass and rigidity, when subjected to strong earthquake ground motions.