考量垂直向效應之多項式摩擦單擺支承之分析與設計

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方嬿甄(Yen-chen Fang) 查詢紙本館藏

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土木工程學系

論文名稱

考量垂直向效應之多項式摩擦單擺支承之分析與設計
(Analysis and Design of Polynomial Friction Pendulum Isolator with Vertical Effect)

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摘要(中)

多項式摩擦單擺支承(Polynomial Friction Pendulum Isolator，PFPI) 為具變頻特性之新型摩擦單擺支承，其曲面函數為一六次方多項式，利用回復勁度遞減之軟化段減緩結構加速度反應，亦可藉由回復勁度遞增之硬化段降低結構位移反應。經研究已證實PFPI可發揮變頻特性，於近域與遠域震波皆發揮良好隔震效果。
若PFPI曲盤硬化段曲面曲率變化急遽，易導致上部結構產生劇烈垂直向運動，改變摩擦面之正向力，因而影響支承摩擦力。然而，前人研究所使用之數值分析法僅考量水平向反應，為了藉由分析模擬含PFPI隔震橋梁之雙向動力反應，本研究考慮水平向與垂直向自由度發展數值分析方法，另考量受水平向及垂直向震波作用及考量橋墩進入非線性行為之結構反應，此外，採用PSO-SA混合式演算法進行多項式摩擦單擺支承與傳統摩擦單擺支承(FPS)最佳參數設計，並比較PFPI與FPS之隔震效益。結果顯示，本研究發展二維數值分析確實可模擬含PFPI隔震橋梁之雙向動力反應，此外，PFPI確實可降低結構受震反應，其減震效能較FPS佳。

摘要(英)

The sliding surface of Polynomial Friction Pendulum Isolator (PFPI) is defined by a sixth-order polynomial function. The restoring force possesses a softening section and a hardening section. In the softening section, the restoring stiffness is decreasing in order to mitigate the structural acceleration response, while in the hardening section, the restoring stiffness is increasing so as to reduce the isolator drift. It has been proven that PFPI is not only able to effectively mitigate the structural seismic response induced by either long period near-fault earthquakes or far-field earthquakes.
However, if the PFPI surface curvature increasing rapidly, it may induce severe structural vertical response. For the purpose of simulating horizontal and vertical responses of the bridge with PFPI, the derivation of analysis method considering horizontal and vertical degree of freedom is developed in this study. Discussion on effects of considering vertical ground excitation and the nonlinear behavior of piers. Moreover, optimal parameter study of PFPI and Friction Pendulum System (FPS) and comparison the effectiveness between PFPI and FPS.
The results show that the derivation of analysis method developed in this study does indeed simulates horizontal and vertical structural seismic responses. Moreover, PFPI is more effective to reduce structural seismic response than FPS.

關鍵字(中)

★ 垂直向震波
★ 摩擦單擺支承
★ 變頻式隔震支承
★ 變曲率隔震支承

關鍵字(英)

★ friction pendulum system
★ vertical ground motion.
★ various frequencies seismic isolator
★ variable-curvature seismic isolator

論文目次

目錄
中文摘要 Ⅰ
英文摘要 Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
表目錄 Ⅷ
圖目錄 Ⅹ
第一章緒論..............................................1
1.1研究背景與動機.........................................1
1.2文獻回顧...............................................3
1.2.1近域震波之特性及隔震結構影響......................3
1.2.2摩擦單擺系統......................................4
1.3研究內容............................................6
第二章多項式摩擦單擺支承................................8
2.1支承力學行為...........................................8
2.2多項式摩擦單擺支承之曲面函數及特性....................12
第三章滑動支承之一維動力分析...........................18
3.1Newmark-β直接積分法..................................18
3.2數值模型及運動方程式推導..............................20
3.2.1支承靜止階段.....................................21
3.2.2支承滑動階段.....................................23
3.3數值分析實例..........................................26
3.3.1目標橋梁.........................................27
3.3.2支承參數及分析震波...............................27
3.3.3分析結果比較與討論...............................28
3.3.4積分時間步幅之比較...............................28
3.4小結..................................................29
第四章滑動支承之二維動力分析...........................41
4.1數值模型及運動方程式推導..............................41
4.1.1支承靜止階段.....................................43
4.1.2支承滑動階段.....................................45
4.1.3上部結構騰空運動.................................50
4.2橋墩非線性之運動推導..................................52
4.3數值分析推導之驗證....................................55
4.3.1實驗試體模型及量測儀器配置.......................55
4.3.2實驗輸入震波.....................................56
4.3.3實驗與數值模擬結果之比對與探討...................56
4.4結構受雙向震波之探討..................................59
4.4.1目標橋梁、支承參數與分析震波.....................59
4.4.2分析結果與探討...................................59
4.5小結..................................................61
第五章 FPS與PFPI最佳參數搜尋及分析結果探討.............105
5.1PSO-SA混合式搜尋法...................................105
5.1.1最佳化問題數學模式之建立........................106
5.1.2粒子群演算法....................................107
5.1.3模擬退火法......................................109
5.1.4PSO-SA混合式搜尋法..............................110
5.2支承最佳化設計.......................................111
5.2.1目標橋梁及分析震波..............................111
5.2.2支承最佳參數搜尋之數學模式......................112
5.2.3支承參數範圍....................................113
5.2.4最佳參數搜尋結果與探討..........................113
5.2.4.1考量橋墩線性................................113
5.2.4.2考量橋墩非線性..............................115
5.2.4.3考量雙向震波................................117
5.2.4.4與文獻[19]最佳參數搜尋結果之比較............117
5.3小結.................................................118
第六章結論與建議.......................................140
6.1結論.................................................140
6.2建議及未來研究方向...................................141
參考文獻................................................143

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指導教授

莊德興(Der-shin Juang)

審核日期

2011-8-24

推文