臺灣博碩士論文加值系統

本研究考慮纜索傾角、纜索初形，以及橋面板與纜索互制效應等三種條件下，執行黏性阻尼器對於斜張橋纜索之減振效用評估。首先，分別建立三者的有限元素模型；接著，進行複數振態分析，分別計算三者之系統於各個振態的自然頻率、阻尼頻率、阻尼比、振動型態，以及阻尼比和黏性阻尼器阻尼係數之關係曲線，由此曲線可決定系統最佳阻尼比與對應的黏性阻尼器最佳阻尼係數；最後，以高屏溪橋為例，同時考慮纜索傾角、纜索初形，以及橋面板和纜索互制效應等三種條件下，執行複數振態分析決定黏性阻尼器最佳阻尼係數後，進行地震歷時分析，針對受地震力作用之系統在未裝設黏性阻尼器，亦即未控制，以及具最佳阻尼係數的黏性阻尼器之被動控制兩種條件下，分別計算其振動反應，以評估黏性阻尼器的減振效用。經由本研究成果可全面地瞭解裝設黏性阻尼器之斜張橋橋面板與纜索互制效應的力學機制，並合理地預測黏性阻尼器之減振效用。

Finite element models of stay cables with attached viscous dampers of cable-stayed bridges are developed in this study. Based on these models, the complex modal analysis is adopted to calculate the natural frequency, damped frequency, damping ratio, mode shape and the curve of damping ratio versus damper coefficient of viscous damper for each mode of the system. The mentioned curve can be provided to determine the optimal damping ratio and the corresponding optimal damper coefficient of viscous damper for each mode of the system. Numerical examples are presented to estimate the optimal parameters of viscous dampers and their effectiveness for vibration control of stay cables with the consideration of the cable inclination, the cable initial shape and the deck-stay interaction of cable-stayed bridges. Under considerations of these optimal parameters, the seismic time history analysis is conducted to calculate the structural responses for two types of systems: without control and passive control, which can be used to assess the effectiveness of viscous damper. The results indicate that the viscous damper with optimal damper coefficient can be applied to effectively reduce the stay cable vibration of cable-stayed bridges.

目錄
摘要....................................................................I
Abstract.............................................................II
致謝....................................................................III
目錄....................................................................IV
表目錄................................................................V
圖目錄................................................................VI
第一章 前言.......................................................1
1.1 研究動機與目的.........................................1
1.2 文獻回顧.....................................................3
1.3 研究內容.....................................................6
第二章 繃緊索加阻尼之理論..........................7
2.1 數學模型.....................................................7
2.2 特殊情形....................................................9
2.3 頻率偏移的阻尼性能.................................12
2.4單一模態行為 .............................................14
第三章 數值算例...............................................16
3.1 纜索傾角.....................................................16
3.2 纜索初形.....................................................17
3.3 橋面板與纜索互制效應.............................22
3.4 高屏溪橋分析.............................................25
第四章 結論與建議..........................................27
4.1 結論.............................................................27
4.2 建議.............................................................28
參考文獻............................................................29

表目錄
表3.1 高屏溪斜張橋各構件分析基本資料.................................................................34
表3.2 高屏溪斜張橋各纜索基本輸入資料.................................................................35
表3.3 受集集垂直地震力作用之高屏溪橋橋塔節點20X方向反應折減率...........36
表3.4 受集集垂直地震力作用之高屏溪橋橋塔節點20Y方向反應折減率...........36
表3.5 受集集垂直地震力作用之高屏溪橋側跨節點35X方向反應折減率...........37
表3.6 受集集垂直地震力作用之高屏溪橋側跨節點35Y方向反應折減率...........37
表3.7 受集集垂直地震力作用之高屏溪橋主跨節點42X方向反應折減率...........38
表3.8 受集集垂直地震力作用之高屏溪橋主跨節點42Y方向反應折減率...........38
表3.9 受集集垂直地震力作用之高屏溪橋纜索節點220X方向反應折減率.........39
表3.10 受集集垂直地震力作用之高屏溪橋纜索節點220Y方向反應折減率.......39
表3.11 受集集垂直地震力作用之高屏溪橋纜索節點296X方向反應折減率.......40
表3.12 受集集垂直地震力作用之高屏溪橋纜索節點296Y方向反應折減率.......40
表3.13 受集集水平地震力作用之高屏溪橋橋塔節點20X方向反應折減率.........41
表3.14 受集集水平地震力作用之高屏溪橋橋塔節點20Y方向反應折減率.........41
表3.15 受集集水平地震力作用之高屏溪橋側跨節點35X方向反應折減率.........42
表3.16 受集集水平地震力作用之高屏溪橋側跨節點35Y方向反應折減率.........42
表3.17 受集集水平地震力作用之高屏溪橋主跨節點42X方向反應折減率.........43
表3.18 受集集水平地震力作用之高屏溪橋主跨節點42Y方向反應折減率.........43
表3.19 受集集水平地震力作用之高屏溪橋纜索節點220X方向反應折減率.......44
表3.20 受集集水平地震力作用之高屏溪橋纜索節點220Y方向反應折減率.......44
表3.21 受集集水平地震力作用之高屏溪橋纜索節點296X方向反應折減率.......45
表3.22 受集集水平地震力作用之高屏溪橋纜索節點296Y方向反應折減率.......45

圖目錄
圖1.1 斜張橋振動型態.....................................................................................................46
圖1.2 斜張橋有限元素模型.............................................................................................47
圖2.1 繃緊纜索裝設線性黏性阻尼器.............................................................................48
圖2.2 純實部特徵值振態.................................................................................................48
圖2.3 非衰減振動.............................................................................................................48
圖2.4 相位方程解(l1/L=0.05，前5個模態)..................................................................48
圖2.5 正規化阻尼比、固定比和正規化阻尼係數關係圖.............................................49
圖2.6 正規化阻尼比與正規化阻尼係數(l1/L=0.05，前8個模態)..............................50
圖2.7 第二個模態阻尼比與頻率和阻尼器位置.............................................................50
圖2.8 三個區域的相位方程解(模態2)...........................................................................51
圖2.9 阻尼係數與振態(l1/L=0.25，第二模態)..............................................................52
圖3.1 考慮傾角之纜索有限元素模型.............................................................................53
圖3.2 纜索傾角介於0°至75°之系統阻尼比與阻尼器係數的關係...............................53
圖3.3 考慮初形之纜索有限元素模型.............................................................................54
圖3.4 纜索中垂量與全長比值等於0％之系統阻尼比與阻尼器阻尼係數的關係.....55
圖3.5 纜索中垂量與全長比值等於0.5％之系統阻尼比與阻尼器阻尼係數的關係..56
圖3.6 纜索中垂量與全長比值等於1％之系統阻尼比與阻尼器阻尼係數的關係.....57
圖3.7 纜索中垂量與全長比值等於1.5％之系統阻尼比與阻尼器阻尼係數的關係..58
圖3.8 纜索中垂量與全長比值等於1.7％之系統阻尼比與阻尼器阻尼係數的關係..59
圖3.9 纜索中垂量與全長比值等於1.9％之系統阻尼比與阻尼器阻尼係數的關係....60
圖3.10纜索中垂量與全長比值等於2％之系統阻尼比與阻尼器阻尼係數的關係......61
圖3.11纜索中垂量與全長比值等於2.1％之系統阻尼比與阻尼器阻尼係數的關係...62
圖3.12纜索中垂量與全長比值等於2.3％之系統阻尼比與阻尼器阻尼係數的關係...63
圖3.13纜索中垂量與全長比值等於2.5％之系統阻尼比與阻尼器阻尼係數的關係..64
圖3.14纜索中垂量與全長比值等於3％之系統阻尼比與阻尼器阻尼係數的關係.....65
圖3.15纜索中垂量與全長比值等於5％之系統阻尼比與阻尼器阻尼係數的關係.....66
圖3.16纜索中垂量與全長比值等於10％之系統阻尼比與阻尼器阻尼係數的關係...67
圖3.17纜索中垂量與全長比值等於15％之系統阻尼比與阻尼器阻尼係數的關係...68
圖3.18纜索中垂量與全長比值等於20％之系統阻尼比與阻尼器阻尼係數的關係... 69
圖3.19系統最佳阻尼比與纜索中垂量和全長比值之關係..............................................70
圖3.20纜索中垂量與全長比值等於0％之系統阻尼比與系統自然頻率的關係..........71
圖3.21纜索中垂量與全長比值等於0.5％之系統阻尼比與系統自然頻率的關係.......72
圖3.22纜索中垂量與全長比值等於1％之系統阻尼比與系統自然頻率的關係..........73
圖3.23纜索中垂量與全長比值等於1.5％之系統阻尼比與系統自然頻率的關係.......74
圖3.24纜索中垂量與全長比值等於1.7％之系統阻尼比與系統自然頻率的關係.......75
圖3.25纜索中垂量與全長比值等於1.9％之系統阻尼比與系統自然頻率的關係.......76
圖3.26纜索中垂量與全長比值等於2％之系統阻尼比與系統自然頻率的關係..........77
圖3.27纜索中垂量與全長比值等於2.1％之系統阻尼比與系統自然頻率的關係.......78
圖3.28纜索中垂量與全長比值等於2.3％之系統阻尼比與系統自然頻率的關係.......79
圖3.29纜索中垂量與全長比值等於2.5％之系統阻尼比與系統自然頻率的關係.......80
圖3.30纜索中垂量與全長比值等於3％之系統阻尼比與系統自然頻率的關係..........81
圖3.31纜索中垂量與全長比值等於5％之系統阻尼比與系統自然頻率的關係..........82
圖3.32纜索中垂量與全長比值等於10％之系統阻尼比與系統自然頻率的關係........83
圖3.33纜索中垂量與全長比值等於15％之系統阻尼比與系統自然頻率的關係........84
圖3.34纜索中垂量與全長比值等於20％之系統阻尼比與系統自然頻率的關係........85
圖3.35區域一之纜索中垂量與全長比值等於0%的系統振動型態................................86
圖3.36區域一之纜索中垂量與全長比值等於1%的系統振動型態................................87
圖3.37區域一之纜索中垂量與全長比值等於2%的系統振動型態................................88
圖3.38區域一之纜索中垂量與全長比值等於3%的系統振動型態................................89
圖3.39區域二之纜索中垂量與全長比值等於0%的系統振動型態................................90
圖3.40區域二之纜索中垂量與全長比值等於1%的系統振動型態................................91
圖3.41區域二之纜索中垂量與全長比值等於2%的系統振動型態................................92
圖3.42區域二之纜索中垂量與全長比值等於3%的系統振動型態................................93
圖3.43區域三之纜索中垂量與全長比值等於0%的系統振動型態................................94
圖3.44區域三之纜索中垂量與全長比值等於1%的系統振動型態................................95
圖3.45區域三之纜索中垂量與全長比值等於2%的系統振動型態................................96
圖3.46區域三之纜索中垂量與全長比值等於3%的系統振動型態................................97
圖3.47纜索中垂量與全長比值等於2% 之第一模態和第二模態..................................98
圖3.48考慮橋面板與纜索互制效應之系統有限元素模型..............................................98
圖3.49考慮橋面板與纜索互制效應之系統各個振態的自然頻率..................................99
圖3.50考慮橋面板與纜索互制效應之系統各個振態的廣義質量..................................100
圖3.51阻尼器裝設於節點9與節點59之間的系統阻尼比和阻尼器阻尼係數的關係..101
圖3.52阻尼器裝設於節點22與節點61之間的系統阻尼比和阻尼器阻尼係數的關係.101
圖3.53阻尼器裝設於節點38與節點63之間的系統阻尼比和阻尼器阻尼係數的關係.101
圖3.54考慮橋面板與纜索互制效應之第4振態系統阻尼比和阻尼器阻尼係數的關係102
圖3.55考慮橋面板與纜索互制效應之第5振態系統阻尼比和阻尼器阻尼係數的關係102
圖3.56考慮橋面板與纜索互制效應之第9振態系統阻尼比和阻尼器阻尼係數的關係103
圖3.57考慮橋面板與纜索互制效應之第10振態系統阻尼比和阻尼器阻尼係數的關係103
圖3.58阻尼器裝設於節點9與節點59之間的系統阻尼比和阻尼器阻尼係數之關係..104
圖3.59阻尼器裝設於節點22與節點61之間的系統阻尼比和阻尼器阻尼係數之關係.104
圖3.60阻尼器裝設於節點38與節點63之間的系統阻尼比和阻尼器阻尼係數之關係.104
圖3.61考慮橋面板與纜索互制效應之第4振態的系統振動型態......................................105
圖3.62考慮橋面板與纜索互制效應之第5振態的系統振動型態......................................106
圖3.63考慮橋面板與纜索互制效應之第9振態的系統振動型態......................................107
圖3.64考慮橋面板與纜索互制效應之第10振態的系統振動型態....................................108
圖3.65高屏溪橋有限元素模型..............................................................................................109
圖3.66高屏溪橋各個振態之自然頻率..................................................................................110
圖3.67高屏溪橋各個振態之廣義質量..................................................................................111
圖3.68阻尼器裝設在纜索S28的系統阻尼比和阻尼器阻尼係數之關係.........................112
圖3.69阻尼器裝設在纜索S19的系統阻尼比和阻尼器阻尼係數之關係.........................112
圖3.70集集地震垂直與水平方向地表加速度......................................................................113
圖3.71受集集垂直地震力作用之高屏溪橋橋塔節點20 X方向歷時反應........................114
圖3.72受集集垂直地震力作用之高屏溪橋橋塔節點20 Y方向歷時反應........................115
圖3.73受集集垂直地震力作用之高屏溪橋側跨節點35 X方向歷時反應........................116
圖3.74受集集垂直地震力作用之高屏溪橋側跨節點35 Y方向歷時反應........................117
圖3.75受集集垂直地震力作用之高屏溪橋主跨節點42 X方向歷時反應........................118
圖3.76受集集垂直地震力作用之高屏溪橋主跨節點42 Y方向歷時反應........................119
圖3.77受集集垂直地震力作用之高屏溪橋纜索節點220 X方向歷時反應......................120
圖3.78受集集垂直地震力作用之高屏溪橋纜索節點220 Y方向歷時反應......................121
圖3.79受集集垂直地震力作用之高屏溪橋纜索節點296X方向歷時反應.......................122
圖3.80受集集垂直地震力作用之高屏溪橋纜索節點296Y方向歷時反應.......................123
圖3.81受集集水平地震力作用之高屏溪橋橋塔節點20 X方向歷時反應........................124
圖3.82受集集水平地震力作用之高屏溪橋橋塔節點20 Y方向歷時反應........................125
圖3.83受集集水平地震力作用之高屏溪橋側跨節點35 X方向歷時反應........................126
圖3.84受集集水平地震力作用之高屏溪橋側跨節點35 Y方向歷時反應........................127
圖3.85受集集水平地震力作用之高屏溪橋主跨節點42 X方向歷時反應........................128
圖3.86受集集水平地震力作用之高屏溪橋主跨節點42 Y方向歷時反應........................129
圖3.87受集集水平地震力作用之高屏溪橋纜索節點220 X方向歷時反應......................130
圖3.88受集集水平地震力作用之高屏溪橋纜索節點220 Y方向歷時反應......................131
圖3.89受集集水平地震力作用之高屏溪橋纜索節點296X方向歷時反應.......................132
圖3.90受集集水平地震力作用之高屏溪橋纜索節點296Y方向歷時反應.......................133

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