Optimal Placement of Dampers in Building Structures Using Response Spectrum Analysis
Date Issued
2012
Date
2012
Author(s)
Huang, Wan-Ting
Abstract
Dampers have been popularly used to retrofit existing building structures and for seismic design of new buildings since Northridge earthquake, The 2011 off the Pacific coast of Tohoku earthquake, and Chi-Chi earthquake. Optimal placement of dampers becomes a hot topic for researchers in structural mechanics and earthquake engineering.
For the past few years, the added dampers are assumed to be placed uniformly at each story of two selected bays. Thus, the damping matrix will be proportional to stiffness matrix or mass matrix. The system is called classical damped system. And it can be decoupled by modal analysis. So that, it could use response spectrum analysis to find the maximum response of the system. When we find the optimal allocation of supplemental dampers, the system will become non-classical damped system. One of the purpose in this research is to extend classical modal analysis to decouple non-classical damped system. First, we decouple the system by phase synchronization. The purpose of phase synchronization is to compensate for the time drifts caused by viscous damping. If suitable phase shifts are introduced into each damped mode of vibration so that all components are either in phase or out of pahse. On the basis of the method, the response spectrum could be derived. The other method that decoupled the non-calssical damped systesm is Laplace transform. In this method, the complex modal analysis is used. And then, use Laplace transform to the complex modal equation. After some processes the decouple system would be found. In phase synchronization, it paired the real eigenvalues by real quadratic conjugation. And in Laplace transform, it didn’t pair the real eigenvalues. So when deriving the response spectrum method for Laplace transformation method, it would be an over-damped mode response spectrum there. The problem of pair eigenvalue in group is to be disscuss in this research.
Finally, the above two response spectrum methods were used in simple method. When using response spectrum method to replace time history analysis, it can reduce most of the analysis time. And the result could be almost the same when it uses the time history analysis in simple method. So that, this method could be used extensively in earthquake engineering.
Subjects
Simple method
decouple
over-damped
complex modal analysis
optimal placement of dampers
response spectrum analysis
phase synchronization method
Laplace transform
Type
thesis
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