Keywords: ground motion record, scaling, shaking table platform, response spectra, optimization criteria.

There are several known methods for scaling earthquake records, allowing a certain decrease in the required shaking table platform's stroke. Scaling in time [1] keeps the form of the given ground acceleration record and its amplitude unchanged, but the spectrum of the scaled acceleration moves to the low natural period range. Centring the ground acceleration or of the ground velocity signal [2] yields no changes in the real earthquake spectrum and reduces the shaking table platform's stroke; however this reduction may be insufficient. In such cases time scaling is used additionally to centring.

A most suitable scaling method should maximally consider the features of the real earthquake record and cause minimum distortion in the earthquake spectrum. Strong earthquakes lead to nonlinear effects in the structural response. Supplementary energy dissipation systems, used for improving structural seismic response, have essentially non-linear characteristics. These facts should be considered during all stages of the design and testing, including the earthquake scaling. The method of scaling the earthquake, proposed in this study, is based on criteria that are more consistent with the nonlinear nature of the structure.

The proposed method is based on a representation of the earthquake record by ground displacement, obtained by double integration of the ground acceleration. The ground velocity is obtained by single integration of the ground acceleration. The desired task is formulated as an equivalent LQR optimization problem.

For verifying the effectiveness of the proposed method the response spectrums of real and simulated earthquakes are compared. Additionally, the response of a multistory structural model to real and simulated seismic records is analysed.

The above procedure was applied to the following earthquakes: El Centro, Hachinohe and Parkfield. The proposed method was used to reproduce the earthquakes by a shaking table with maximal platform stroke of ±6 cm. It is shown that using the proposed method allows more accurate reproduction of the ground motion.

The response of a six-storey steel frame to original and scaled earthquakes was analysed. The responses of the analysed structure to both the original and scaled earthquake are close each to other, which demonstrates the effectiveness of the proposed method.

1

UCIST Shake Table, User's manual, Quanser Consulting Inc., Canada, 2000.

2

B. Blostotsky, Y. Ribakov, G. Agranovich, "Adaptation of real earthquake records for their reproduction by a shaking table with the limited stroke", Earthquake Engineering and Engineering Vibration, 9, 493-502, 2010. doi:10.1007/s11803-010-0031-3

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