一般而言，大垮度拱橋是作為人行天橋良好的選擇。這是因為橋樑的型態，不僅能滿足運輸需求，也可能成為當地的標誌性建築。在這些人行天橋中，因為橋面版較為狹窄，故單拱是唯一的選擇。由於單拱缺乏側向支撐，並由於橋跨距長度的高度增加，橋拱的拖曳向反應較為顯著，不能忽略。基於顫振理論、抖振理論及斷面模型試驗測得的顫振導數，將作用在拱圈上的風力放入運動方程式進行顫振和抖振分析的推導。如此一來，預測出來的空氣動力學反應對於橋梁的初步設計很有幫助。 

    本文採用人行吊索拱橋作為例題，來證明這種方法的有效性和適用性。從數值模擬結果，作用在橋上的顫振風速的拱上的力的影響進行討論。該結果表明，作用在拱圈的風力將增加整個拱橋的顫振臨界風速。

The long-span arch bridges have been a favorable choice for the design of pedestrian bridges during the past decades in Taiwan. This is because the type of bridges not only can satisfy the transportation needs but also may become the landmark in the local area. In these pedestrian bridges, a single arch is the only choice due to the narrow bridge deck. Since the single arch lacks lateral support and its height increases with the bridge span length, the drag responses in the arch become significant and cannot be negligible. An analytical approach based on flutter and buffeting theory associated with the information measured from section model tests is presented in this thesis. The wind forces action on the arch are incorporated into the derivation of the multi-mode equations for flutter and buffeting analysis. Using this approach, the predicted aerodynamic responses can be obtained and may be helpful for the preliminary design. 
    An arch bridge with a straight bridge girder is used as an example to demonstrate the validity and applicability of this approach. From the numerical results, the effects of the forces acting on the arch on the flutter wind speed of the bridge are discussed. The results show that the addition of wind forces acting on the arch will increase the flutter wind speed of the whole bridge.

目錄
第一章　緒論	1
1-1 研究目的與動機	1
1-2 研究方法	2
1-3 論文架構	3
第一章　緒論	3
第二章　文獻回顧	3
第三章　拱橋顫振理論推導	3
第四章　拱橋抖振理論推導	3
第五章　人行拱橋顫振數值分析	3
第六章　結論與建議	3
第二章　文獻回顧	4
2-1 人行拱橋近代發展	4
2-2 橋梁氣動力效應	5
2-2.1顫振效應（Flutter）	5
2-2.2抖振效應（Buffeting）	7
2-2.3 渦流顫振（Vortex Shedding）	8
2-2.4扭轉不穩定現象（Torsion Instability）	8
2-2.5風馳效應（Galloping）	9
2-3 拱橋氣動力研究發展	10
第三章　拱橋顫振理論推導	11
3-1 前言	11
3-2 運動方程式建立	11
3-3 拱橋顫振理論推導	15
3-3-1 橋面版與橋拱自身擾動力	15
3-3-2 顫振臨界風速	20
第四章　拱橋抖振分析	28
4-1 橋面版及橋拱抖振擾動力	28
4-2 風力頻譜	33
4-3 橋面版與橋拱風力頻譜	37
4-3.1 橋面版垂直向抖振擾動力	37
4-3.2橋面版拖曳向抖振擾動力	40
4-3.3橋面版扭轉向抖振擾動力	41
4-3.5橋拱拖曳向抖振擾動力	45
4-3.6橋拱扭轉向抖振擾動力	46
4-3.7橋面版與橋拱垂直向抖振擾動力	47
4-3.9橋面版與橋拱扭轉向抖振擾動力	49
4-4 抖振位移反應	49
第五章　人行拱橋顫振數值分析	52
5-1　單拱單索面人行吊索拱橋之顫振數值分析	52
5-1.1　結構形式	52
5-1.2　模態分析	53
5-1.3　顫振臨界風速分析	54
5-2　單拱雙索面人行吊索拱橋之顫振數值分析	55
5-2.1　結構形式	55
5-2.2　模態分析	55
5-2.3　顫振臨界風速分析	56
第六章　結論與建議	58
6-1　結論	58
6-2　建議	58
附表	59
附圖	65
參考文獻	69

 
表目錄

表3- 1　顫振導數代表之物理意義	59
表5- 1　單拱單索面吊索拱橋斷面性質	60
表5- 2　單索面與雙索面纜索性質	60
表5- 3　單拱單索面人行拱橋動力分析	61
表5- 4　單拱單索面人行拱橋考慮橋拱受風反應以及未考慮橋拱受風反應之臨界風速及頻率(顫振導數取自文獻【22】)	62
表5- 5　單拱雙索面吊索拱橋斷面性質	62
表5- 6　單拱雙索面人行拱橋動力分析	63
表5- 7　單拱雙索面人行拱橋考慮橋拱受風反應以及未考慮橋拱受風反應之臨界風速及頻率(顫振導數取自文獻【22】)	64

 
圖目錄
圖3- 1　全域座標系統	65
圖3- 2　橋面版座標系統	65
圖3- 3　橋拱座標系統	66
圖3- 4　橋拱局部座標系統	66
圖5- 1　單拱單索面拱橋	66
圖5- 2　單索面與雙索面纜索連接形式	67
圖5- 3　橋面版顫振導數，取自文獻【22】	67
圖5- 4　橋拱顫振導數P1*~P3*，由Scanlan【23】理論計算之	68

第二章
【1】Keil, A., “Design Of Footbridges - Are There Limits?, ” Footbrige, 2008.
【2】Meier, U., “Advanced Composite Materials For Footbridges,” Footbrige, 2008.
【3】 Scanlan, R. H., Tomko, J. J., “Airfoil and Bridge Deck Flutter Derivatives,” Journal of Engineering Mechanical Division, ASCE, Vol. 97, pp.1717-1737 1971.
【4】Simiu, E., Scanlan, R. H., “Wind Effects on Structures ,” John Wiley & Sons. 1986.
【5】 Kazama, K., Yamada, H. and Miyata, T., “Wind Resistant Design for Long Span Suspension Bridges,” Journal of Wind Engineering and Industrial Aerodynamics, No. 54/55, pp.65-74 (1995)
【6】 謝政宏,“氣動力參數對長跨徑橋梁顫振臨界風速的影響 ”,私立淡江大學土木工程研究所碩士論文(1999).
【7】Hikami, Y., Shiraishi, N., “Rain-Wind Induced Vibrations of Cable Stayed Bridges,”Journal of Wind Engineering and Industrial Aerodynamics, Vol. 29, pp.409-418(1988).
【8】Yoshimura, T., Savage, M. G., Tanaka, H., and Wakasa, T., “A device for suppressing wake galloping of stayed-cables for cable-stayed bridges,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp.497-506, 1993.
【9】黃明慧,“曲線斜張橋之氣動力穩定研究,” 私立淡江大學土木工程研究所碩士論文, 2005.
【10】 Katz, C., Kovacs, I., and Morgenthal, G., “Three-dimensional aerodynamic and aeroelastic Analysis of the pedestrian bridge,” D-A-CH Tagung, 2003.
【11】Li, J., Bai, H., and Liu, J., “Experimental Investigation Into Aerodynamic Stability Of A Narrow Bridge For Pedestrian And Livestock,” The Seventh Asia-Pacific Conference, 2008.
【12】Kala, J., Bajer, M., and Barnat , J., “Numerical Simulation Of Dynamic Wind Load Of The Foot-Bridge,”Recent Researches In Geography, Geology, Energy, Environment And Biomedicine, 2011.

第三章
【13】Scanlan, R. H.,“Interpreting Aerolastic Models of Cable-Stayed Bridges,”Journal of Engineering Mechanics, ASCE, Vol. 113(4), pp. 555-576(1987).
【14】Tanaka, H., Yamamura, N. and Tatsumi, M., “Coupled Mode Flutter Analysis Using Flutter Derivatives,”Journal of Wind Engineering and Industrial Aerodynamics, Vol. 41-44, pp.1279-1290(1992).
【15】	李鳳娟,“振態耦合對大跨度橋梁自勵振動現象之影響,”私立淡江大學土木工程研究所碩士論文,1995.
第四章
【16】Kaimal, J. C., “Spectrum Charactertics of Surface-Layer Turbulence, ” J. Royal Meteorol. Soc., 98, pp.563-589, 1972. 
【17】Davenport, A.G., “The Dependence of Wind Load upon Metrorological Parameters,” Proceedings of the Tnternational Research Seminar on Wind Effects on Buildings and Structure,University of Toronto,pp. 19-82(1968)
【18】Vickery, B. J., “On the Reliability of Gust Loading Factors,” Proceedings of the Technacal Meeting Concerning Wind Loads on Buildings and Structures, National Bureau of Standards, Building Science Series 30, Washington, D.C.,pp. 93-104(1970)
【19】Lumley, J. L. and Panofsky, H. A., “The Structure of Atmospheric Turbulence”, Wiley, New York, 1964.
【20】Liepmann, R. W., “On the application of statistical concept to the buffeting problem, ” J. Aero. Sci ., Vol.19, No.12 , 1952.
【21】Vickery, B. J., “On the flow behind a coarse gris and its use a modal of atomspheric turbulence in studies related to wind load on building, ” N. P. L. Aero. Report 1143, 1965.
第五章
【22】Scanlan. R.H.,Tomko J.J.,"Airfoil and Bridge Deck Flutter Derivatives",Journal of Eng.Mech.Div.,Vol,97	pp.1717-1737  (1971) fig.8,No.3
【23】Scanlan. R.H.,"Interpreting Aerolastic Models of Cable-Stayed Bridges,"J.Engrg.Mech., ASCE,113(4), pp. 555-576(1987)