Response spectrum analysis for non-classically damped linear system with multiple-support excitations |
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| Authors: | Rui-Fang Yu Xi-Yuan Zhou |
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| Institution: | (1) Institute of Geophysics, China Earthquake Administration, Mingzu Daxue South Road No. 5, Haidian District, Beijing, 100081, P.R. China;(2) Beijing Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Pingleyuan No.100, Beijing, 100022, P.R. China |
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| Abstract: | A new response spectrum method, which is named complex multiple-support response spectrum (CMSRS) method in this article,
is developed for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-supported
ground motion. The CMSRS method is based on fundamental principles of random vibration theory and properly accounts for the
effect of correlation between the support motions as well as between the modal displacement and velocity responses of structure,
and provides an reasonable and acceptable estimate of the peak response in term of peak seismic ground motions and response
spectra at the support points and the coherency function. Meanwhile, three new cross-correlation coefficients or cross covariance
especially for the non-classically damped linear structures with multiple-supports excitations are derived under the same
assumptions of the MSRS method of classically damped system. The CMSRS method is examined and compared to the results of time
history analyses in two numerical examples of non-classically damped structures in consideration of the coherences of spatially
variable ground motion. The results show that for non-classically damped structure, the cross terms representing the cross
covariance between the pseudo-static and dynamic component are also quite small just as same as classically damped system.
In addition, it is found that the usual way of neglecting all the off-diagonal elements in transformed damping matrix in modal
coordinates in order to make the concerned non-classically damped structure to become remaining proportional damping property
will bring some errors in the case of subjected to spatially excited inhomogeneous ground motion. |
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| Keywords: | Non-classical damping Multiple-support excitations Response spectrum Seismic ground motion |
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