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研究生:邱瑜燕
研究生(外文):Yu-Yen Chiu
論文名稱:結構強震數據之系統識別與應用研究
論文名稱(外文):A Study on System Identification and Engineering Applicationof Strong Motion Records in Buildings
指導教授:姚昭智姚昭智引用關係
指導教授(外文):G.C.Yao
學位類別:博士
校院名稱:國立成功大學
系所名稱:建築學系碩博士班
學門:建築及都市規劃學門
學類:建築學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:122
中文關鍵詞:反共振頻率系統識別基本反共振頻率共振頻率遞迴式ARX模型ARX模型A FMM方法
外文關鍵詞:resonant frequencyAFMM methodARX modelRARX modelsystem identificationanti-resonant frequency
相關次數:
  • 被引用被引用:8
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  • 收藏至我的研究室書目清單書目收藏:3
本研究乃針對建築物強震數據建立一套系統識別方法,並將此法應用在各種不同案例分析上,以分析強震作用下的建築物不同頻率內涵或加速度之振動特質及工程應用上之特性。本文所建立系統識別之方法具有多重檢核與可依訊號內涵分類分析等優點,且估計誤差非常小。由於加入AFMM方法,使系統分析振動信號時,可有效截取時變區段以遞迴式ARX分析時變反應,以縮短估計初始試誤時段。

本研究探討之振動信號取自於實際強震記錄與破壞性試驗兩種,前者是由瑞里地震、集集地震與嘉義地震發生時,PGA在80gal(震度五級)以上的RC結構物動力量測資料組成;後者則是以擬白噪音、台北盆地(TAP)與台中盆地(TCU-078)自由場的歷時記錄為輸入訊號,輸入強度由小至大能使試體破壞的振動台試驗。以這些振動信號所構成的分析組合為:(1)以75組建築物強震儀觀測歷時記錄利用AFMM方法分析強震作用下系統何時進入時變反應,並以ARX模型求出系統非時變反應的頻率與阻尼比,其中37組則進一步以遞迴式ARX模型求出系統時變反應的頻率。(2)以400組破壞性試驗歷時記錄利用AFMM方法分析強震作用下系統何時進入時變反應,並以ARX模型求出系統非時變反應的頻率與阻尼比,其中94組再進一步以遞迴式ARX模型求出系統時變反應的頻率。(3)以384筆歷時記錄分析樓板反應譜。系統識別所分析的頻率無論時變系統與否均包含第一、二模態共振頻率及第一模態反共振頻率。

假設所分析樣本皆為線性動態概率集中參數離散系統時,可得結論如下:
1. 當建築物結構愈不對稱時,扭矩效應的影響會增加。
2. 強震作用下之建築物最好先以A FMM方法觀察是否有時變區段發生,線性非時變區段可以ARX模型分析,線性時變區段宜以遞迴式ARX模型分析。
3. 樓層基本反共振頻率在建築物的中高樓層處可以避開時變區段第一模態共振頻率,但是在低樓層部分則不一定能避免與第一模態頻率之重合。
4. 樓層基本反共振頻率隨著試體破壞程度增加而降低,頻率遞減趨勢大致上與第一、二模態共振頻率相同。
5. 根據含牆RC構架試驗結果可知,基本反共振頻率做為設備物耐震設計的有效性,可能在與第一模態共振頻率發生重疊前的結構狀態。
The purpose of this research is to establish a new system identification method and the application of the identified system data. This method has the advantages of multiple checking and data sorting in analysis, and the error of estimation is small.

The analyzed data come from two parts: first part is the building strong motion records in Taiwan with PGA greater than 80 gal from Ra-Li, Chi-Chi, and Chia-Yi earthquakes. Second part is nonlinear test data from shaking table tests. This includes input of pseudo white noise, TAP and TCU-078 ground motion. The analysis is constituted of: (1)Seventy-five pairs of building strong motion records are used to analyze the beginning of time-varying response of buildings in earthquakes by the AFMM method. Their frequencies and damping ratios are identified by the ARX model. Thirty-seven pairs among them are identified by the RARX (Recursive-ARX) model, to identified the frequencies and damping ratios in the time-varying response. (2)The 400 pairs of nonlinear laboratory test data are used to analyze the beginning of time-varying response of buildings in strong earthquakes by the AFMM method. By the ARX model, the frequencies and damping ratios are identified. Ninety-four pairs among them are identified by the RARX model to distinguish the frequencies and damping ratios of the time-varying response. (3)Three hundred eighty four time history records are used to analyze floor response spectrum. All of the analysis include the first and second mode resonant frequencies and the first anti-resonant frequencies.

Assuming all the sample data are linear, dynamic, stochastic, lumped-parameter, discrete-time systems, conclusions can be summarized below:
1. The more asymmetric the structural form of a building is, the more the torsional effect exists.
2. The building strong motion records would be best examined by the AFMM method to observe whether there is a time-varying response region. ARX model for the linear time-invariant region system ID is suitable while the linear time-varying region is best analyzed by the RARX model.
3. Only at the upper floors, the fundamental anti-resonant frequency(ARF)will not move beyond the first resonant frequency in time-varying region.
4. The decrease trend of the first and second natural frequencies in damaged buildings is close to that of the fundamental anti-resonant frequency.
5. From the laboratory tests of RC frame-wall buildings, the appropriate structural behavior to choose the ARF approach in equipment protection is before the overlapping of the ARF and the fundamental frequencies take place.
摘要………………………………………………..………..…………....….. i
Abstract………………………………………………..………..…………… ii
誌謝………………………………………………..………..………….....… iii
目錄……………………………………………….……..….…………….... iv
圖目錄……………………………………………….……..……………... vii
表目錄……………………………………………….……..……….……….. x
符號說明……………………………………………..……..………………. xi
Abbreviations…………………………………………………………… ..viii

第一章 緒論………………………………………………………………..1
1-1 研究動機與目的………………………………………………………..1
1-2 文獻回顧………………………………………………………………..2
1-2-1 系統識別理論
1-2-2 基本振動週期識別與分析
1-2-3 非時變反應之反共振頻率分析與應用
1-2-4 強震作用時變反應分析
1-2-5 破壞性試驗分析
1-2-6反應譜分析
1-3 研究方法………………………………………………………………..8

第二章 系統識別理論…………….………………..…………………...12
2-1 動力方程式…………………………………………..…………..……14
2-2 系統識別理論之應用………………………………..…………..……15
2-3 ARX模型…………………………………………………….…..……16
2-4 遞迴式ARX模型………………………………………………..……17
2-5 AFMM方法…………………………………….………………..……18
2-6 無損建築物小地震與弱震區段識別結果之比較……………..…..…19
2-7 SAP2000與ARX識別結果之比較……………..……………………22
2-8 時變反應合理性之探討……………..……………………………..…25


第三章 強震作用下模態頻率特性……………..…………………..27
3-1 AFMM方法分析………………………………………………..……28
3-2 結構基本振動週期分析……………………..…………………..……31
3-2-1 ARX模型
3-2-2 基本振動週期建議公式
3-3 基本反共振頻率分析…………………………………..………..……37
3-3-1 ARX模型
3-3-2 未明顯損壞之建築物
3-3-3 非結構牆具明顯損壞之建築物
3-4 時變反應下之反共振頻率頻率特性…………………..………..……44
3-4-1 未明顯損壞之建築物
3-4-2 非結構牆具明顯損壞之建築物
3-4-3 案例分析結果
3-5 小結…………………………………..………..……………………....51

第四章 破壞試驗頻率特性……………………………..…………53
4-1 試體及試驗過程簡介………………………….………………..……53
4-2 ARX模型識別……………………………………..…………..60
4-3 純梁柱RC構架試體分析……………..…………………..………65
4-4 含RC牆RC構架試體分析…………………………..…………70
4-5 含磚牆RC構架試體分析………………...………..…………….76
4-6 小結…………………………………….………..……….……81

第五章 建築物頻率對設備反應之影響………………..……………84
5-1 樓高放大係數…………………………………………………..……..84
5-2 設備共振反應放大係數………………………………………..……..86
5-3 設備共振反應放大係數與樓層高度比之關係………………..……..91
5-4 基本反共振頻率對系統反應之影響…………………………..……..96
5-5 小結……………………………………………………………..……..98


第六章 結論……………………………………………..…………99
6-1 結論………………………………………...………..…………99
6-2 後續研究……………………………………………..………. 100

附錄:建築物加速度測計配置圖…………………..………………….. 102
參考文獻……………………………………………..…………….. 117
自傳……………………………………………..………..…….……121
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