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                                       Details for article 6 of 7 found articles
 
 
  Mode Superposition Method of Non Stationary Seismic Responses for Non Classically Damped Linear Systems
 
 
Title: Mode Superposition Method of Non Stationary Seismic Responses for Non Classically Damped Linear Systems
Author: Zhou, Xi-Yuan
Yu, Rui-Fang
Appeared in: Journal of earthquake engineering
Paging: Volume 12 (2008) nr. 3 pages 473-516
Year: 2008-03
Contents: The real earthquake ground accelerations are usually non stationary vibration process. In order to estimate the influence of the non stationarity of ground motion on the accuracy of modal superposition rule of complex complete quadratic combination (CCQC), a new time-dependent CCQC(t) algorithm is derived by using a determinate envelope function to modulate a stationary random white noise process and remaining other assumptions same as normal CQC method. The proposed time-dependent CCQC(t) method needs to calculate the variances, covariance, and cross variances for different modes as time functions. For CCQC(t) method, the cross variances between a pair of two different modes are usually named cross correlation coefficients and play very important role in estimation of maximum responses just as for CQC method, but in this case the cross correlation coefficients are time dependent. Moreover, CCQC(t) and CQC(t) methods need to define envelop function and to calculate the corresponding non stationary seismic response rather than CCQC and CQC methods where only stationary steady-state responses are concerned. Hence, the analyses and computations related to envelop function in CCQC(t) and CQC(t) methods also play very a important role in this article. Several closed form formulas of time-dependent variances and cross variances are derived by using integration technique developed in time domain for four popularly used envelope functions. In order to verify these closed form formulas deduced in this article, we use four different envelope functions to fit identical envelope curve of real acceleration time history and then to carry out numerical analyses for certain examples. The numerical analysis based on proposed CCQC(t) algorithm shows that all the seismic responses of the examples computed from the adopted four different envelope functions which are used to depict same envelop curve of input acceleration are almost the same. The example analyses also show that for normal structure and ground motion input the discrepancy of the maximum seismic responses calculated from CCQC(t) and CCQC methods for non classically damped linear system and that from CQC(t) and CQC methods for classically damped linear system is of insignificance because the occurrence times of the variance responses and cross covariance responses usually concentrate within very narrowed time interval and close to the peak value location of the input motion at time axis. Further analyses show that the significance of the non stationarity mainly depends on how far the peak value arrival times of the modal responses shift each other and how sharper the shape of the envelop of input motion. Generally speaking, the larger the peak values arrival time shift and the sharper the shapes of the different modal response envelops, the greater the influence of non stationarity of ground motion on the results of mode superposition based on response spectra. These results are obtained on the basis of white noise input assumption. In addition, it is also shown that if using colorful spectrum such as Kanai power spectrum density function to replace white noise to simulate the power spectrum of the input acceleration records, the results coming from both CCQC(t) and CCQC methods may be improved to certain degree.
Publisher: Taylor & Francis
Source file: Elektronische Wetenschappelijke Tijdschriften
 
 

                             Details for article 6 of 7 found articles
 
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