本論文的研究內容為比較和檢驗由簡化式所得之顫振臨界風速與抖振反應和精確理論式間之差異。選用三種不同斷面與跨徑的橋樑結構為例，檢驗簡化式與理論式所得結果之差異。計算顫振臨界風速時，選用中國規範、日本規範和奧地利規範所用之簡化式，再加上Selberg的理論作檢驗。利用參數影響分析改變垂直與扭轉的頻率，比較在不同頻率比下對於橋樑顫振臨界風速的影響。其結果顯示，各種簡化式的顫振臨界風速都比理論式來的保守，當中以日本的公式最為保守，Selberg的公式最接近用理論分析計算出的結果。
相較於顫振臨界風速的計算，抖振反應的計算就相當複雜與冗長，也因此只有極少數的簡化式被提出來過。中國規範提出的方法，仍然是一個相當複雜的設計方式。所以此方法計算的結果與理論式相近。由於此方法的簡化不多，再加上所使用之橋樑其結構耦合效應並不顯著，因此所得結果與抖振理論相近。因此簡化式只能適用於橋樑的初始設計，對於受風敏感的橋樑，還是須經由更精確的分析與風洞實驗來檢驗。

Some simplified formulae for the prediction of flutter critical wind speeds and buffeting responses were examined and compared to the precise theories in this study. Three bridge models, with different bridge decks and spans, were chosen as the examples. For the simplified flutter analysis, three formulae respectively used in the Chinese code, Japanese design manual and Austrian code and one proposed by Selberg were examined. The effects of vertical and torsional frequencies on the flutter critical wind speeds were also studied through a parametric analysis. The results show that all the flutter critical wind speeds calculated from the four simplified formulae are lower than those from flutter theory. Among them, the formula used in the Japanese manual is the most conservative and the Selberg formula is the closest to flutter theory.

Since the buffeting calculation is more complex and tedious than the calculation of flutter critical wind speed, there are few simplified formulae proposed. In the Chinese code, the proposed method is still complex for the engineers. The results obtained from the Chinese code are close to buffeting theory. It can be expected because there are few simplifications in this method and the structural coupling are not significant in the example bridges. It should be mentioned that the simplified analysis is better used for the preliminary design. If the bridge is sensitive to wind, more precise analysis should be performed.

目錄
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 研究內容 2
1.4 論文架構 3
第二章 文獻回顧 5
2.1 前言 5
2.2 橋樑風力效應之探討 5
2.2.1 扭轉不穩定(Torsional instability) 6
2.2.2 渦流振動(Vortex shedding) 6
2.2.3 風馳效應(Galloping) 7
2.2.4 顫振(Flutter) 8
2.2.5 抖振(Buffeting) 9
2.2.6 風力係數 10
2.2.7 顫振導數(Flutter derivative) 10
2.3 橋樑斷面形狀 11
2.3.1 流線型與非流線型 11
2.3.2 斷面寬深比 12
2.3.3 斷面加設物 12
2.3.4 整流片(fairing) 13
2.3.5 結語 14
第三章 顫振理論與分析模式 15
3.1 前言 15
3.2 顫振理論 15
3.2.1 顫振擾動力 15
3.2.2 橋樑運動方程式 16
3.2.3 橋樑顫振臨界風速分析方法 18
3.3 顫振簡化分析 24
3.3.1 中國的顫振簡化式 24
3.3.2 日本的顫振簡化式 25
3.3.3 奧地利的顫振簡化式 26
3.3.4 Selberg的顫振簡化式 26
第四章 抖振理論與分析模式 28
4.1 前言 28
4.2 抖振理論 28
4.2.1 抖振擾動力（Buffeting force） 28
4.2.2 抖振效應之分析 29
4.3 抖振簡化分析 41
4.3.1 Scanlan的抖振簡化式 42
4.3.2 中國的抖振簡化式 43
第五章 斷面模型實驗與數值模式介紹 49
5.1 前言 49
5.2 斷面模型 49
5.2.1 斷面模型之製作 49
5.2.2 斷面模型之轉動慣量 50
5.3 實驗流程 51
5.3.1 單自由度實驗(非耦合向導數) 51
5.3.2 雙自由度實驗(耦合向導數) 51
5.3.3 靜力實驗(風力系數) 51
5.4 實驗儀器介紹 52
5.4.1 壓力轉換器 52
5.4.2 皮托管 (Pitot Tube) 52
5.4.3 模型受力量測-應變片及應變訊號放大器 53
5.4.4 振動位移量測-雷射測距儀 54
5.5 數值模式 55
5.5.1 橋樑一 55
5.5.2 橋樑二 56
5.5.3 橋樑三 57
第六章 結果與討論 58
6.1 前言 58
6.2 顫振臨界風速之分析 58
6.2.1 簡化式與理論分析之比較 59
6.2.2 改變垂直頻率對顫振之影響 60
6.2.3 改變扭轉頻率對顫振之影響 61
6.3 各種斷面對顫振之影響 61
6.4 抖振位移反應分析 62
6.4.1 垂直向之抖振分析比較 62
6.4.2 扭轉向之抖振分析比較 63
第七章 結論與建議 64
7.1 結論 64
7.2 建議 65



附表
表2.1 顫振導數代表之物理意義 71
表5.1 橋樑一主梁斷面性質 72
表5.2 橋樑一橋塔斷面性質 72
表5.3 橋樑一鋼纜斷面性質 73
表5.4 橋樑一數值模型之前10振態 73
表5.5 橋樑二主梁斷面性質 74
表5.6 橋樑二橋塔斷面性質 74
表5.7 橋樑二鋼纜斷面性質 75
表5.8 橋樑二數值模型之前10振態 75
表5.9 橋樑三數值模型之前10振態 76
表6.1 各種顫振臨界風速之比較 76
表6.2 橋樑一於各種垂直頻率之顫振臨界風速 77
表6.3橋樑二於各種垂直頻率之顫振臨界風速 77
表6.4 橋樑三於各種垂直頻率之顫振臨界風速 78
表6.5 橋樑一於各種扭轉頻率之顫振臨界風速 78
表6.6 橋樑二於各種扭轉頻率之顫振臨界風速 79
表6.7 橋樑三於各種扭轉頻率之顫振臨界風速 79
表6.8 橋樑一於各種斷面之顫振臨界風速 80
表6.9 橋樑一各種斷面之顫振臨界風速與簡化式之比較 80
表6.10 橋樑二於各種斷面之顫振臨界風速 81
表6.11 橋樑二各種斷面之顫振臨界風速與簡化式之比較 81
表6.12 橋樑三於各種斷面之顫振臨界風速 82
表6.13 橋樑三各種斷面之顫振臨界風速與簡化式之比較 82


附圖
圖2-1 斷面模型受風下的自由度表示 83
圖2-2 橋樑扭轉不穩定示意圖 83
圖2-3 各類型斷面之顫振導數 84
圖3-1 數值模擬之橋樑斷面受風力示意圖 84
圖3-2 斷面形狀修正函數 85
圖3-3 日本實驗的顫振臨界風速 85
圖5-1 顫振導數之實驗架構圖 86
圖5-2 拖曳向風力係數〔CD〕量測架構圖 87
圖5-3 垂直向與扭轉向風力係數〔CL、CM〕量測架構圖 88
圖5-4 皮托管量測風速之儀器配置圖 89
圖5-5 橋樑一幾何示意圖 90
圖5-6 橋樑一斷面之鋼構造部份（steel section） 90
圖5-7 橋樑一斷面之混凝土部份（concrete section） 91
圖5-8 橋樑二幾何示意圖 91
圖5-9 橋樑二之斷面模型 92
圖5-10 橋樑三幾何示意圖 92
圖5-11 橋樑三之斷面模型 92
圖6-1.1 橋樑一之顫振導數 93
圖6-1.2 橋樑一之顫振導數 94
圖6-2.1 橋樑二之顫振導數 95
圖6-2.2 橋樑二之顫振導數 96
圖6-3.1 橋樑三之顫振導數 97
圖6-3.2 橋樑三之顫振導數 98
圖6-4 橋樑一於各種垂直頻率比的顫振臨界風速 99
圖6-5 橋樑二於各種垂直頻率比的顫振臨界風速 99
圖6-6 橋樑三於各種垂直頻率比的顫振臨界風速 100
圖6-7 橋樑一於各種扭轉頻率比的顫振臨界風速 100
圖6-8 橋樑二於各種扭轉頻率比的顫振臨界風速 101
圖6-9 橋樑三於各種扭轉頻率比的顫振臨界風速 101
圖6-10 橋樑一垂直向最大抖振反應 102
圖6-11 橋樑二垂直向最大抖振反應 102
圖6-12 橋樑三垂直向最大抖振反應 103
圖6-13 橋樑一扭轉向最大抖振反應 103
圖6-14 橋樑二扭轉向最大抖振反應 104
圖6-15 橋樑三扭轉向最大抖振反應 104

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