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Shock and Vibration
Volume 2017, Article ID 2046345, 11 pages
https://doi.org/10.1155/2017/2046345
Research Article

Computation of Rayleigh Damping Coefficients for the Seismic Analysis of a Hydro-Powerhouse

State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China

Correspondence should be addressed to Zhiqiang Song; moc.621@4002qihzs

Received 12 April 2017; Accepted 27 July 2017; Published 30 August 2017

Academic Editor: Xing Ma

Copyright © 2017 Zhiqiang Song and Chenhui Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The mass and stiffness of the upper and lower structures of a powerhouse are different. As such, the first two vibration modes mostly indicate the dynamic characteristics of the upper structure, and the precise seismic response of a powerhouse is difficult to obtain on the basis of Rayleigh damping coefficients acquired using the fundamental frequencies of this structure. The damping ratio of each mode is relatively accurate when the least square method is used, but the accuracy of the damping ratios that contribute substantially to seismic responses is hardly ensured. The error of dynamic responses may even be amplified. In this study, modes that greatly influence these responses are found on the basis of mode participation mass, and Rayleigh damping coefficients are obtained. Seismic response distortion attributed to large differences in Rayleigh damping coefficients because of improper modal selection is avoided by using the proposed method, which is also simpler and more accurate than the least square method. Numerical experiments show that the damping matrix determined by using the Rayleigh damping coefficients identified by our method is closer to the actual value and the seismic response of the powerhouse is more reasonable than that revealed through the least square method.