By using the second GPS method to study structure response signal under earthquakes
Date Issued
2014
Date
2014
Author(s)
Wang, Hung-Cheng
Abstract
Most of engineering problems can be formulated in the form of ordinary differential equations (ODEs). Nowadays, people usually use numerical analysis to find an approximate solution when the exact solution of ODEs is hard to derive. The group preserving scheme (GPS) developed by Liu is a numerical method based on group theorem. It is a stable and accurate method for solving ODE because in every step of GPS, it can retain the group structure in a Lorentz group form. The present thesis mainly introduces the concept of Jordan structure to modify the original augmented dynamic system of GPS, hence a more accurate numerical method, named the second type of GPS (GPS2) comes up, and in the example there will show the comparison between GPS2 and other methods, like the GPS and the famous RK4 method. Moreover, it is interesting that we can find signal barcodes reflected to the characteristics of the system, and the barcodes are generated by signum function through the process of using GPS2 to solve ODEs. Consequently, by applying the GPS2 to solve SDOF motion equation under earthquakes and classifying the sign in order to realize both physical meaning and the switch of the sign in detail can construct a bridge between the signal barcode and the structural response, as a result, we can abstract the information by scanning barcodes. In this thesis, we will not only describe the basic theory of GPS2 but also write a program to simulate the response of SDOF system and its signal barcode under different earthquakes by MATLAB. After that, there are some conclusions and future works at last.
Subjects
李群
李代數
保群算法
喬登結構
第二類保群算法
符號函數
單自由度運動方程式
Type
thesis
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