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研究生:藍倉連
研究生(外文):Tsang-Lien Lan
論文名稱:斷面寬深比對長跨徑橋梁顫振與抖振之影響
論文名稱(外文):Effect of B/D Ratio of Section on Flutter and Buffeting of Long-Span Bridges
指導教授:林堉溢
指導教授(外文):Yuh-Yi Lin
學位類別:碩士
校院名稱:淡江大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:144
中文關鍵詞:長跨徑橋梁斷面寬深比顫振抖振效應無因次化風速複數特徵值法
外文關鍵詞:long-span bridgeB/D ratio of sectionflutterbuffetingreduced velocitycomplex eigenvalue method
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隨著高強度的工程材料與施工技術有相當大的進步,促使橋梁結構系統趨向於長跨徑為基本型態,橋梁斷面的設計必須更為輕薄細長,因此長跨徑橋梁具更大之柔度,風力作用的效應更是大幅提高,尤其是橋體的顫振行為與抖振效應。顫振行為是指橋梁結構受風作用產生自身擾動力,而引發的氣動力勁度與氣動力阻尼,與結構慣性力、阻尼及內力產生互制效應,在某一臨界風速下,消散結構阻尼,導致橋梁結構的破壞。抖振效應則是逼近流的速度擾動,對結構系統形成不穩定載重,而使結構產生振動現象。
橋梁結構系統的顫振行為與抖振效應,不僅與橋梁斷面幾何形狀有關,斷面寬深比的改變對於顫振與抖振亦造成影響。本文即在探討橋梁斷面寬深比的改變對顫振導數及風力係數之影響。乃以風洞物理模型實驗來求取不同寬深比的橋梁斷面在平滑流場中的顫振導數與風力係數,再根據實驗所得之顫振導數與風力係數,利用數值分析之方法探討寬深比的改變對橋梁結構系統之顫振臨界風速與抖振效應的影響,最後再將數值分析之結果提出分析與探討。
由本文研究所得之結果顯示,斷面寬深比的改變對橋梁結構系統的氣動力穩定度有明顯的影響。以流線型斷面而言,寬深比的改變會影響臨界風速,即寬深比越大,臨界風速越高,且隨著寬深比的增加,耦合效應也越明顯。而非流線型的斷面,寬深比的改變對臨界風速造成相當大的影響,即隨著寬深比的降低,臨界風速遞減的非常明顯,但對於耦合效應並無明顯影響。而抖振效應亦隨斷面寬深比的改變而改變。因此斷面寬深比的改變對於氣動力穩定度變化亦為橋梁設計時考量的關鍵。
The developments of bridge construction techniques and the improvements of high strength materials have made the modern bridges designed and built towards long spans with slender sections. Because these types of bridges are more flexible than the other types of bridges, they are more sensitive to wind excitations. The most significant aerodynamic phenomenon for long-span bridges includes flutter and buffeting. Self-excited forces, bridges induced by deck motions, will result in aerodynamic stiffness and aerodynamic damping. When the negative aerodynamic damping is equal to the structural damping at some wind speed, the flutter will occur, that is, the bridge will result in failure. Buffeting response is mainly induced by the wind turbulence.
Flutter critical wind speed and buffeting of the bridge system are not only related to the geometry of bridge deck but also the width-depth ratio of the deck section. In this thesis, section model tests were conducted to investigate the effects of different width-depth ratios on flutter derivatives and wind force coefficients in smooth flow. Based on the test data, the critical wind speed and buffeting were then evaluated by using numerical analysis method.
The results show that the changes of width-depth ratios have significant influence on aerodynamic stability of long span bridges. With the increase of width-depth ratio, the flutter critical wind speed and coupling effect will increase for streamline section. However, the changes of width-depth ratio have no significant influence on coupling effect for bluff sections. The width-depth ratios also affect buffeting responses on bridge structures. Therefore, effects of width-depth ratio of the deck section on aerodynamic stability should be taken into account in the bridge design.
目錄
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 研究項目 3
1.4 研究方法 4
1.4.1 第一階段為橋梁模型的風洞實驗 4
1.4.2 第二階段為數值分析5
1.5 本文架構 5
第二章 文獻回顧 7
2.1 前言 7
2.2 風力係數與顫振導數的研究 7
2.2.1 風力係數 8
2.2.2 顫振導數(Flutter Derivative) 9
2.2.2.1 斷面型式的影響10
2.2.2.2 斷面寬深比的影響12
2.2.2.3 護欄型式的影響13
2.2.2.4 風攻角的影響13
2.3 風洞試驗之文獻回顧14
2.3.1 端板效應(End Plate Effect):14
2.3.2 阻塞比效應(Blockage Ratio Effect): 15
第三章 長跨徑橋梁風力效應之探討 17
3.1 前言17
3.2長跨徑橋梁之風效應18
3.2.1顫振效應(Flutter)18
3.2.1.1 顫振導數之推導19
3.2.2抖振效應(Buffeting)23
3.2.2.1 風力係數23
3.2.3渦流顫振(Vortex Shedding)25
3.2.4 扭轉不穩定現象(Torsion Instability)26
3.2.5風馳效應(Galloping)26
3.3 顫振與抖振效應的數值分析模式27
3.3.1橋體外力介紹27
3.3.1.1 顫振擾動力27
3.3.1.2 抖振擾動力(Buffeting force)28
3.3.2 橋梁結構運動方程式之建立29
3.3.3 橋梁振態耦合臨界風速分析方法32
3.3.4 抖振效應之分析36
3.3.4.1 風力交頻譜的推導36
3.3.4.2 橋梁受風載重之位移反應42
第四章 氣彈模型模擬、儀器介紹與取樣分析45
4.1 前言45
4.2 大氣邊界層之風洞實驗45
4.2.1風洞實驗室的特性45
4.3橋梁氣彈模型之模擬46
4.3.1 斷面模型(Deck Section Model)簡介46
4.3.2 氣彈力模型相似律47
4.3.3 實驗模型之應用47
4.3.4 斷面模型之縮尺48
4.3.5 斷面模型之製作49
4.3.6 斷面模型在風洞中的位置50
4.4 實驗儀器介紹50
4.4.1 風速量測(Measuring Wind Velocity)50
4.4.1.1 微壓計50
4.4.1.2 壓力轉換器51
4.4.1.3 皮托管 (Pitot Tube)51
4.4.1.4 熱膜探針(Hot Film Probe)52
4.4.2 受力量測-應變片及應變訊號放大器53
4.4.3 位移量測-雷射測距儀54
4.5實驗配置流程55
4.5.1風力係數的實驗流程55
4.5.2顫振導數的實驗流程55
4.6 模型之數據採樣與分析55
4.6.1 數據採樣55
4.6.2 數據分析56
第五章 風洞實驗架構及實驗結果討論57
5.1 前言57
5.2 實驗內容57
5.3 實驗架構58
5.3.1 模型架設58
5.3.2 斷面模型之自然頻率及阻尼比之率定58
5.3.3模型轉動慣量之求得59
5.4 實驗方法60
5.4.1 靜力實驗之風力係數60
5.4.1.1拖曳向風力係數CD的架構60
5.4.1.2 垂直向與扭轉向風力係數CL、CM的架構60
5.4.2 動態實驗之顫振導數61
5.4.2.1 垂直向非耦合導數(H1*)的求取61
5.4.2.2 扭轉向非耦合導數(A2*, A3*)的求取62
5.4.2.3 耦合導數(H2*, H3*, A1*)的求取62
5.5 實驗結果與討論63
5.5.1風力係數之實驗結果63
5.5.1.1 Model_1風力係數之比較64
5.5.1.2 Model_2風力係數之比較66
5.5.2 顫振導數之實驗結果68
5.5.2.1 Model_1顫振導數之比較68
5.5.2.2 Model_2顫振導數之比較72
第六章 顫振臨界風速與抖振效應之數值分析75
6.1 前言75
6.2 數值模型的建立75
6.2.1 幾何形狀75
6.2.2 斷面性質75
6.2.3 結構特性模擬76
6.2.4 數值結構之基本振態分析76
6.3 臨界風速分析76
6.3.1 Model 1-3、胡與高屏溪橋之顫振臨界風速比較77
6.3.2 Model_1之顫振臨界風速比較77
6.3.3 Model_2之顫振臨界風速比較78
6.4 抖振分析79
6.4.1 Model_1之抖振分析比較80
6.4.2 Model_2之抖振分析比較81
第七章 結論與建議82
7.1結論 82
7.2建議83
附表目錄
表 2-1 顫振導數代表之物理意義93
表 4-1 Model_1之各斷面性質比較94
表 4-2 Model_2之各斷面性質比較95
表 6-1 高屏溪橋主梁斷面性質 96
表 6-2 高屏溪橋橋塔斷面性質 96
表 6-3 高屏溪橋鋼纜斷面性質 97
表 6-4 高屏溪橋數值模型之前十振態97
表 6-5 Model_1配合高屏溪橋數值模型之顫振臨界風速分析結果 98
表 6-6 Model_2配合高屏溪橋數值模型之顫振臨界風速分析結果 99
表 6-7 高屏溪橋於設計風速52m/s垂直與扭轉向之最大抖振反應比較 100
表 6-8 Model_1在風速為52m/s之各方向最大抖振反應101
表 6-9 Model_2在風速為30m/s之各方向最大抖振反應102
附圖目錄
圖 1-1 Tacoma Narrow Bridge 發生顫振(flutter)的情形 103
圖 2-1 橋梁斷面受風力示意圖 104
圖 2-2 各型橋梁斷面的風力係數與顫振導數之(一) 105
圖 2-3 各型橋梁斷面的風力係數與顫振導數之(二) 106
圖 3-1 扭轉不穩定之幾何示意圖 107
圖 3-2 數值模擬之橋梁斷面受風力示意圖 107
圖 4-1 淡江大學大氣邊界層風洞實驗室配置圖 108
圖 4-2 高屏溪橋原型斷面之鋼構造部份(steel section) 109
圖 4-3 高屏溪橋原型斷面之混凝土部份(concrete section) 111
圖 4-4 Model 1-1∼1-4之斷面幾何形狀圖 112
圖 4-5 Model 2-1~2-4之斷面幾何形狀圖 113
圖 4-6 Model_1與Model_2斷面模型完成圖 114
圖 4-7 斷面模型於風洞實驗室之架設圖 115
圖 4-8 皮托管量測風速之儀器配置圖 116
圖 4-9 應變計之率定曲線圖 117
圖 4-10 風力係數與顫振導數之實驗儀器配置流程圖 118
圖 5-1 Model 1-3 與Model 2-3之轉動慣量計算圖 119
圖 5-2 拖曳向風力係數〔CD〕量測架構圖 120
圖 5-3 垂直向與扭轉向風力係數〔CL、CM〕量測架構圖 121
圖 5-4 顫振導數之實驗架構圖 122
圖 5-5 Model_1 於平滑流場中之拖曳向風力係數比較圖 123
圖 5-6 Model_1 於平滑流場中之垂直向風力係數比較圖 124 圖 5-7 Model_1 於平滑流場中之扭轉向風力係數比較圖 125
圖 5-8 Model_2 於平滑流場中之拖曳向風力係數比較圖 126
圖 5-9 Model_2 於平滑流場中之垂直向風力係數比較圖127
圖 5-10 Model_2 於平滑流場中之扭轉向風力係數比較圖128
圖 5-11 Model_1於平滑流場中之H1*顫振導數比較圖129
圖 5-12 Model_1於平滑流場中之A2*顫振導數比較圖130
圖 5-13 Model_1於平滑流場中之A3*顫振導數比較圖131
圖 5-14 Model_1於平滑流場中之H2*顫振導數比較圖132
圖 5-15 Model_1於平滑流場中之H3*顫振導數比較圖133
圖 5-16 Model_1於平滑流場中之A1*顫振導數比較圖134
圖 5-17 Model_2於平滑流場中之H1*顫振導數比較圖135
圖 5-18 Model_2於平滑流場中之A2*顫振導數比較圖136
圖 5-19 Model_2於平滑流場中之A3*顫振導數比較圖137
圖 5-20 Model_2於平滑流場中之H2*顫振導數比較圖138
圖 5-21 Model_2於平滑流場中之H3*顫振導數比較圖139
圖 5-22 Model_2於平滑流場中之A1*顫振導數比較圖140
圖 6-1 高屏溪橋之幾何形狀 142
圖 6-2 高屏溪橋橋塔立面圖 142
圖 6-3 高屏溪橋數值模型示意圖 143
圖 6-4 高屏溪橋數值模型配合Model_1實驗參數在設計風速為52m/s
(α=0°)之抖振反應 144
圖 6-5 高屏溪橋數值模型配合Model_1實驗參數在不同風速下(α=0°)
各方向最大抖振反應 144
圖 6-6 高屏溪橋數值模型配合Model_2實驗參數在設計風速為30m/s(α
=0°)之抖振反應 146
圖 6-7 高屏溪橋數值模型配合Model 2-1∼2-2實驗參數在不同攻角下各
方向抖振反應 147
圖 6-8 高屏溪橋數值模型配合Model 2-3∼2-4實驗參數在不同攻角下各
方向抖振反應 148
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