隨著橋樑工程的快速發展，近代的懸索支撐橋樑除了基本的交通功能外，
外型上的設計也越來越多元，曲線造型的設計亦是相當常見的設計。當曲線橋
體結構受風作用時，其風向角是沿著橋軸而變化，若以有限元素的觀點來看，
亦即表示每一節塊桿件與來流之間的風向角均不相同，正因如此，一般會將其
視為橋樑受斜風作用的衍生。在過去經常使用餘弦法則(Cosine Rule)以及斜風理
論(Skew Wind Theory)等近似方法來模擬此些不同風向角下的節塊斷面之風效
應，但是，這些近似理論僅能適用於小風向角或是低風速的情況下。
本文旨在針對曲線結構發展一套完整且較為嚴謹的顫振理論與抖振理論。
曲線理論中直接以斷面風洞實驗方式考慮不同風向角下之氣動力參數，而不以
近似方法進行模擬。文中亦設計一座曲率半徑及夾角分別為250m 及60°的曲線
斜張橋樑，其斷面則採用寬深比為5 之矩形斷面，並以縮尺全模型風洞實驗的
方式來驗證比較本文所提出曲線理論。
實驗結果顯示，在無初始風攻角以及風向角的情況下，曲線斜張橋樑的顫
振臨界風速約為85.38 m/s，本文所提出之曲線理論與餘弦近似方法的預估差距
均在1%以內。就抖振反應而言，餘弦近似法在高風速下高估了橋體垂直向擾動
均方根值；曲線理論與餘弦近似法對於拖曳向擾動均方根值均有良好的預估結
果；兩方法均高估了高風速下的扭轉向擾動均方根值，特別是餘弦近似法，此
高估現象極有可能是因為紊流削減了氣動力阻尼A2
*對結構扭轉阻尼的影響

Attributed to the developments of bridge engineering, modern cable-supported bridge
design requires not only the needs of transportation but also the aesthetical appearance. As
the curved bridge is subjected to wind excitation, the yaw angles along the bridge axis are
continuously varied because of the curved appearance. In other words, the yaw angle of each
deck element is different in the finite element analysis. Therefore, the wind effects on the
curved bridges can be regarded as the further applications of straight bridges under various
yaw winds. In conventional analysis, the “Cosine Rule” and the “Skew Wind Theory” were
often used for dealing with these effects. However, these approximate theories were
demonstrated valid only for small yaw angles or low wind speeds.
This study aims at developing a reasonable theory for flutter and buffeting analysis of
the curved bridge. The proposed method is based on the aerodynamic coefficients and the
flutter derivatives obtained from section model tests for different yaw angles. In order to
demonstrate the validity and applicability of the theory, a curved cable-stayed bridge was
designed and the full aeroelastic model test was conducted. A rectangular cross section with
the width-to-depth ratio of 5 was adopted for the bridge. The curvature and the included angle
of the target are 250 m and 60°, respectively.
The experimental results show that the critical flutter wind speed is about 85.38 m/s. The
numerical predictions obtained from both the proposed theory and the Cosine Rule are less
than 1%. For the buffeting responses, the Cosine Rule overestimates the vertical responses
especially at high wind velocities. The results obtained from both the proposed theory and the
Cosine Rule agree well with the experimental results in the drag direction. However, both the
proposed method and the Cosine Rule overestimate the torsional responses. The phenomenon
is more obvious for the results predicted from the approximate method. The possible reason
for the discrepancies in the torsional responses is that the negative aerodynamic damping is
overestimated in the section model test under smooth flow.

目 錄............................................... I
表目錄.............................................. IV
圖目錄.............................................. V
第一章 緒論......................................... 1
1.1 前言............................................ 1
1.2 研究動機與目的.................................. 2
1.3 研究方法與內容.................................. 3
第二章 文獻回顧..................................... 5
2.1 前言............................................ 5
2.2 橋樑風力效應.................................... 5
2.2.1 顫振效應( Flutter )與顫振導數................. 5
2.2.2 抖振效應( Buffeting )與風力係數............... 6
2.2.3 扭轉不穩定( Torsional instability )........... 7
2.2.4 渦流振動( Vortex shedding )................... 7
2.2.5 風馳效應( Galloping )......................... 8
2.3 直橋斜風效應.................................... 8
2.3.1 風向角效應.................................... 8
2.3.2 餘弦法則(Cosine Rule) ........................ 10
2.3.3 斜風理論(Skew Wind Theory).................... 11
2.4 曲線橋風效應.................................... 13
第三章 理論背景..................................... 14
3.1 前言............................................ 14
3.2 曲線橋樑座標系統與運動方程式.................... 14
3.2.1 曲線橋樑座標系統.............................. 14
3.2.2 橋樑運動方程式................................ 15
3.3 曲線橋顫振理論.................................. 16
3.3.1 顫振擾動力.................................... 17
3.3.2 橋樑顫振臨界風速分析方法...................... 20
3.4 曲線橋抖振理論.................................. 23
3.4.1 抖振擾動力.................................... 23
3.4.2 橋樑抖振反應分析方法.......................... 27
3.5 系統識別方法(System Identification)............. 31
3.5.1 亞伯拉罕時域法(Ibrahim Time Domain, ITD) ..... 32
3.5.2 修正亞伯拉罕時域法(MITD)...................... 35
第四章 實驗設置介紹................................. 39
4.1 前言............................................ 39
4.2 風洞特性........................................ 39
4.3 實驗儀器介紹.................................... 40
4.4 數據擷取........................................ 41
4.5 相似率轉換...................................... 42
第五章 斷面模型實驗................................. 44
5.1 前言............................................ 44
5.2 斷面模型設計與製作.............................. 44
5.3 風力係數實驗設置與結果.......................... 45
5.4 顫振導數實驗設置與結果.......................... 47
5.5 小結............................................ 49
第六章 全縮尺模型實驗............................... 51
6.1 前言............................................ 51
6.2 全縮尺模型設計與製作............................ 51
6.2.1 全縮尺模型設計................................ 51
6.2.2 全縮尺模型製作................................ 52
6.3 實驗設置........................................ 53
6.4 縮尺模型結構特性識別............................ 53
6.5 邊界層流場設置.................................. 55
6.6 顫振臨界風速實驗結果............................ 56
6.7 抖振反應實驗結果................................ 56
第七章 數值分析與全模型試驗結果之比較............... 59
7.1 前言............................................ 59
7.2 有限元素模型與其修正............................ 59
7.3 顫振臨界風速結果與比較.......................... 60
7.4 抖振反應結果與比較.............................. 61
7.5 小結............................................ 65
第八章 結論與建議................................... 66
8.1 結論............................................ 66
8.2 建議............................................ 68
參考文獻............................................ 69

表目錄
表2.1 傳統顫振導數之物理意義........................ 75
表2.2 曲線理論顫振導數之物理意義.................... 76
表6.1 縮尺模型振態與識別結果........................ 77
表6.2 邊界層流場之紊流強度.......................... 77
表7.1 標的橋樑斷面原始參數.......................... 78
表7.2 顫振臨界風速數值與全模型試驗結果之比較........ 78
表7.3 數值抖振預估與全模型試驗結果之差距百分比...... 78

圖目錄
圖 1.1 研究內容與方法流程圖......................... 79
圖 2.1 扭轉發散幾何示意圖........................... 80
圖 2.2 餘弦分解法幾何示意圖......................... 80
圖 2.3 餘弦法則與實驗值比較(Zhu，【18】) ........... 81
圖2.4 斜風理論幾何示意圖............................ 81
圖3.1 曲線橋理論座標示意圖.......................... 82
圖3.2 i-th 節點受風示意圖(XZ 平面).................. 82
圖3.3 平均風力座標示意圖............................ 83
圖3.4 i-th 節點初始風角示意圖(XZ 平面).............. 83
圖3.5 ITD 位移反應矩陣組成架構...................... 84
圖3.6 ITD 之特徵值分佈圖............................ 84
圖5.1 斷面風力係數實驗架構示意圖.................... 85
圖5.2 斷面風力係數實驗架構圖........................ 85
圖5.3 BD5 風力係數 (1) ............................. 86
圖5.3 BD5 風力係數 (2) ............................. 87
圖5.4 斷面顫振導數實驗架示意圖...................... 88
圖5.5 斷面顫振導數實驗架示意圖...................... 88
圖5.6 B/D=5 斷面之顫振導數
      (a)H1(b)H4c)A2(d)A3(e)H2(f)H3(g)A1(h)A4....... 92
圖6.1 虛擬標的物橋樑示意圖.......................... 93
圖6.2 縮尺模型骨架示意圖............................ 93
圖6.3 實驗設置示意圖................................ 94
圖6.4 實驗設置圖.................................... 94
圖6.5 縮尺模型YG 向之振態形狀與識別結果............. 95
圖6.6 縮尺模型ZG 向之振態形狀與識別結果............. 96   
圖6.7 縮尺模型XG 向之扭轉振態形狀與識別結果......... 97
圖6.8 縮尺模型垂直向自由振動歷時.................... 98
圖6.9 縮尺模型扭轉向自由振動歷時.................... 98  
圖6.10 縮尺模型位移反應譜(識別)..................... 99 
圖6.11 平滑流場之風速剖面........................... 100
圖6.12 邊界紊流場之流場特性......................... 100
圖6.13 邊界紊流場下橋面板中心處之無因次化風速頻譜... 101  
圖6.14 平滑流場下B00 處之扭轉反應(β0=0°，α0=0°)..... 102
圖6.15 α0= 0°時邊界紊流場下縮尺模型之垂直向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 103  
圖6.16 α0=+3°時邊界紊流場下縮尺模型之垂直向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 104
圖6.17 α0= -3°時邊界紊流場下縮尺模型之垂直向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 105
圖6.18 α0= 0°時邊界紊流場下縮尺模型之拖曳向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 106
圖6.19 α0=+3°時邊界紊流場下縮尺模型之拖曳向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 107
圖6.20 α0= -3°時邊界紊流場下縮尺模型之拖曳向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 108
圖6.21 α0= 0°時邊界紊流場下縮尺模型之扭轉向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 109
圖6.22 α0=+3°時邊界紊流場下縮尺模型之扭轉向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 110
圖6.23 α0= -3°時邊界紊流場下縮尺模型之扭轉向反應(a)β0=0°
      (b)β0=10° (c)β0=20° (d)β0=30° ................ 111
圖7.1 邊界紊流場B00 處之數值結果比較
    (a)垂直向(b)拖曳向(c)扭轉向..................... 112
圖7.2 邊界紊流場N15 與P15 處之數值結果比較
    (a)垂直向(b)拖曳向(c)扭轉向..................... 113
圖7.3 不同風速下之垂直向位移反應頻譜
    (a)B00,U=3.815m/s(b)B00,U=5.047m/s
    (c)B00,U=6.183m/s(d)N15,U=3.815m/s
    (e)N15,U=5.047m/s(f) N15,U=6.183m/s............. 114 
圖7.4 不同風速下之拖曳向位移反應頻譜
    (a)B00,U=3.815m/s(b)B00,U=5.047m/s 
    (c)B00,U=6.183m/s(d)N15,U=3.815m/s 
    (e)N15,U=5.047m/s (f) N15,U=6.183m/s............. 115
圖7.5 不同風速下之扭轉向位移反應頻譜
    (a)B00,U=3.815m/s(b)B00,U=5.047m/s 
    (c)B00,U=6.183m/s (d)N15,U=3.815m/s 
    (e)N15,U=5.047m/s (f) N15,U=6.183m/s............. 116 
圖7.6 5 m/s 之橋面板垂直向數值抖振分析結果........... 117 
圖7.7 5 m/s 之橋面板拖曳向數值抖振分析結果........... 117 
圖7.8 5 m/s 之橋面板扭轉向數值抖振分析結果........... 117

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