論文提要內容：
近代科技的發展，使得橋樑的跨徑逐漸的增長，橋樑的斷面受氣動力效應的影響也隨著跨徑的增加而遞增，長跨徑橋樑受風產生的自身擾動力，會引發氣動力勁度與氣動力阻尼，而氣動力阻尼將會抵消橋樑結構的阻尼，使得橋樑於顫振臨界風速產生了發散而破壞。
橋樑的顫振現象起因於風效應下產生的自身擾動力，而自身擾動力受各方向的氣動力參數所影響，而氣動力參數是根據橋樑斷面的幾何形狀由實驗而得，因此若能了解產生顫振時，各氣動力參數對顫振臨界風速的影響程度，就可以有效的避免橋樑顫振現象的發生。以一般方法分析橋樑顫振臨界風速並無法清楚的了解各氣動力參數對顫振現象的影響程度，因此本文將介紹複數特徵值法與扭轉頻率逐步迭代法的分析流程與理論公式的推導，並且以實例分析來探討各氣動力參數對顫振臨界風速所佔有的重要性、跨徑變化(結構頻率)和扭轉頻率與垂直頻率比(ωα/ωy )對顫振臨界風速的影響。
對於非耦合之單自由度顫振橋樑，其主要產生原因為A2 由負值反轉為正值的時候；而耦合顫振橋樑主要為A1 、A2、 H3 的耦合效應影響，此外隨著跨徑變小或頻率比(ωα/ωy )的提高將會提高橋樑的顫振臨界風速。

Abstract：
The developments of bridge construction techniques have led to the wide use of long span in bridges. The effects of aerodynamic forces on such bridges increase significantly with the span length. While the negative aerodynamic damping is equal to the structural damping at some wind speed, the flutter phenomenon will occur, that is, the bridge will result in failure.
The flutter can be attributed to the self-excited forces that are commonly expressed by flutter derivatives, which are measured from section model tests. For the case of one degree-of-freedom flutter, the effects of A2 is known as the most important. However, for the case of coupled flutter, the flutter derivatives are related to each other, the influence of each individual flutter derivative on critical wind speed is difficult to justify by the previous methods. In this study, an iterative approach is used to investigate the effect of each flutter derivative on critical wind speed. By using this method, the aerodynamic damping resulted from each flutter derivative can be calculated and the influence of each flutter derivative on coupled flutter can be better understood. The applicability and validity of this method are examined by a comparison between the complex eigenvalue method and this present method. Through a parametric study, the effects of flutter derivatives, the ratio of the first torsional frequency to the first vertical frequency, and bridge span length on flutter wind speed are investigated.
The results show that the effects of A1 ,A2 ,A3 and H3 on critical wind speed of coupled flutter are more significant than the other flutter derivatives. The increase of the ratio of the first torsional frequency to the first vertical frequency and the decrease of bridge span length can increase the critical wind speed.

目 錄I
附表目錄III
附圖目錄IV
第一章 緒 論1
1-1 研究動機與目的1
1-2 文獻回顧2
1-2.1氣動力參數( Flutter Derivatives )2
1-2.2顫振( Flutter )臨界風速之研究4
1-3 本文內容7
第二章 長跨徑橋樑之風效應9
2-1 前言9
2-2 風場特性之介紹9
2-2.1 平均風速剖面（ Mean Velocity Profile ）10
2-2.2 亂流強度（ Turbulence Intensity ）11
2-2.3 亂流頻譜（ Turbulence Power Spectrual Density ）12
2-3 橋樑受風力之現象探討17
2-3.1 扭轉發散（ Torsional divergence ）18
2-3.2 渦流顫動（ Vortex shedding ）19
2-3.3 風馳效應（ Galloping ）19
2-3.4 顫振（ Flutter ）20
2-3.5 亂流效應（ Buffeting ）21
第三章 橋樑振態耦合臨界風速分析方法23
3-1 前言23
3-2 橋體運動方程式的建立23
3-2.1 橋體自身擾動力23
3-2.2 橋體運動方程式25
3-3 橋樑結構之顫振臨界風速的建立27
3-3.1 複數特徵值法27
3-3.2 扭轉頻率逐步迭代法 ( Step by Step Analysis )32
第四章 氣動力參數對橋樑顫振臨界風速之影響42
4-1 前言42
4-2 橋樑之分析模型43
4-2.1 古典顫振橋樑A之分析模型43
4-2.2 單自由度顫振橋樑B之分析模型44
4-2.3 高屏溪橋樑之分析模型45
4-3氣動力參數(A1、A2、A3、H1、H2、H3)與顫振臨界風速的關係 47
4-3.1 氣動力參數(A1、A2、A3、H1、H2、H3)與耦合橋樑A之顫振臨界風速的關係48
4-3.2 氣動力參數(A2、A3、H1)與非耦合橋樑B之顫振臨界風速的關係 52
4-3.3 氣動力參數對高屏溪橋的影響54
4-4 結構頻率對耦合顫振臨界風速之影響55
4-4.1 跨徑變化與顫振臨界風速的關係55
4-4.2 扭轉向與垂直向頻率比對顫振臨界風速的關係56
第五章 結論與展望58
5-1 結論58
5-2 展望60
附 表62
附 圖77
參 考 文 獻99

1. Nobuto, J., Fujino, Y. and Ito, M., "A Study on the effectiveness of TMD to suppress s coupled Flutter of Bridge Deck," Journal of JSCE, October, pp. 413-416(1988).
2. Agar, T.J. A.,"The Analysis of Aerodynamic Flutter of Suspension Bridges," Computer & Structures, Vol. 30, NO. 3, pp. 593-600 (1988)
3. Agar, T.J. A.," Aerodynamic Flutter Analysis of Suspension Bridges by a Modal Technique," Eng. Struct., Vol. 11, pp. 75-82 (1989)
4. M., Gu and H. F., Xiang, "Optimization of TMD for Suppressing Buffeting Response of Long-span Bridges," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 41-44, pp. 1383-1392 (1992).
5. M., Gu, H. F., Xiang and A. R., Chen, "A practical method of TMD for suppressing wind-induced vertical buffeting of long-span cable-stayed bridges and its application," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 51, pp. 203-213 (1994).
6. Scanlan, R. H. and Gade, R. H., "Motion of Suspended Bridge Spans under Gusty Wind," Journal of the Structural Division, ASCE, pp. 1867-1883 (1977).
7. Scanlan, R. H. and Jones, N. P., "Aeroelastic Analysis of Cable-Stayed Bridges," Journal of Structural Engineering, ASCE, Vol. 116, No. 2, pp. 279-297 (1990).
8. Scanlan, R. H. and Jones, N. P., "Minimun Design Methodology for Evaluating Flutter and Buffeting Response," Journal of Wind Engineering and Industrial Aerodynamic, Vol. 36, pp. 1341-1353 (1990).
9. Bucher, C. G. and Y. K., Lin, "Stochastic Stability of Bridges Considering Coupled Modes," Journal of Engineering Mechanics, ASCE, Vol. 114, No. 12, pp. 2064-2067 (1988)。
10. Bucher, C. G. and Y. K., Lin, "Stochastic Stability of Bridges Considering Coupled Modes," Journal of Engineering Mechanics, ASCE, Vol. 115, No. 2, pp. 384-400 (1989)。
11. 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).
12. Namini, A. , Albrecht, P. and Bosch, H., "Finite Element-Based Flutter Analysis of Cable-Suspended Bridges," Journal of Structural Engineering, ASCE Vol. 118, No.6, pp. 1509-1927 (1992).
13. W. L., Qu and H. F., Xiang, "An Analysis Method for Buffeting Response of Flexible Bridge with Aerodynamic Coupling Between Modes," Proceedings of the Third Asia-Pacific Symposium on Wind Engineering, pp. 181-185.
14. Bratt, J. B. and Scruton, C., "Measurement of Pitching Moment Derivatives for an Aerofoil Oscillating about the HalfChord Axis," British Aerodynautical Research Council, R.& M., No. 1921 (1938).
15. Bratt, J. B. and Wight, K. D., "The Effect of Mean Incidence, Amplitude of Oscillation, Profile, and Aspect Ratio on Pitching Moment Derivatives," British Aerodynatutical Research Council, R.,& M., No. 2064 (1946).
16. Halfman, R. L., "Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow," NACA Technical Report, 1108 (1952).
17. Scanlan, R. H. and Sabzevari, A., "Suspension Bridge Flutter Revisited," ASCE Structural Engineering Conference (1967).
18. Scanlan, R. H. and Tomko, J. J., "Airfoil and Bridge Deck Flutter Derivatives," Journal of Eng. Mech. Div., ASCE, Vol. 97, pp. 1717-1737 (1971).
19. Scanlan, R. H., "Interpreting Aerolastic Models of Cable-Stayed Bridges," Journal of Engineering Mechanics, ASCE, 113(4), pp. 555-576 (1987).
20. Sears, W. R., "Some aspects of non-stationary airfoil theory and its practical applications," J. Aero. Sci., Vol. 8, No. 2 (1941).
21. Liepmann, R. W., "On the application of statistical concept to the buffeting problem," J. Aero. Sci ., Vol. 19, No. 12 (1952).
22. Davenport, A. G., "The Buffeting of a Suspension Bridge by Storm Winds," Proc. ASCE, Journal of the Structural Division, Vol. 88, pp.233-268 (1962).
23. Vickery, B. J., "On the flow behind a coarse gris and its use a modal of atmospheric turbulence in studies related to wind load on building," N. P. L. Aero. Report 1143 (1965).
24. Jancaskas, E. D. and Melbourne, W. H., "The Aerodynamic Admittance of Two-Dimensional Rectangular Section Cylinders in Smooth Flow," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 23, pp. 395-408 (1986).
25. Honda, A., Shiraishi, N., Matsumoto, M., Fuse, Y., Sumi, K. and Sasaki, N., "Aerodynamic stability of Kansai International Airport Access Bridge," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp. 533-542 (1993).
26. Den Hartog, J. P. Mechanical Vibration, 4th ed., McGraw-Hill, New York, (1956).
27. Jacquot, G. and Hoppe, D. H., "Optimal random vibration absorbers," Journal of Eng. Mech. Div., Vol. 99, pp. 612-616 (1973).
28. Wirsching, H. and Campbell, G. C., "Minimal structure response under random excitation using the vibration absorber," Earthquake Engineering and Structural Dynamics, Vol. 2, pp. 303-312 (1974).
29. Warburton, B., "Optimum absorber parameters for various combinations of response and excitation parameters," Earthquake Engineering and Structural Dynamics, Vol. 10, pp. 381-401 (1982).
30. Jensen, Hector , Setareh, Mehdi and Peek, Ralf ,"TMDs for Vibration Control of Systems with Ucertain Properties," Journal of Structural Engineering, ASCE, Vol. 118, No. 12, December, (1992).
31. Slori, G., "Along-wind Response Estimation : Closed Form Solution," Journal of Structural Division, ASCE, Vol. 108, No.ST1, pp. 225-244 (1982).
32. Ioi, T. and Ikeda, K., "On the dynamic vibration damped absorber of the vibration system," Bull. JSME, 64 (1978)
33. Igusa, T. and Xu, K., "Wide band-response characteristics of multiple subsystems with high modal density," Proc. 2nd int. Conf. stochastic struct. dyn. Florida, U.S.A. (1990).
34. Yamaguchi, H. and Harnpornchai, N., "Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations," Earthquake Engineering and Structural Dynamics, Vol. 22, pp. 51-62 (1993).
35. Kareem, Ahsan and Kline, Samuel, "Performance of Multiple Mass Dampers Under Random Loading," Journal of Structural Engineering. ASCE, Vol. 121. No. 2, February, (1995).
36. Abe, M. and Fujino, Y., "Dynamic characterization of multiple tuned mass dampers and some design formulas," Earthquake Engineering and Structural Dynamics, Vol. 23, pp. 813-835 (1994).
37. Simiu, E. and Scanlan, R. H. Wind Effects on Structures, 2nd ed. John Wiley & Sons.(1986)
38. Hikami, Y. and Shiraishi, N., "Rain-Wind Induced Vibrations of Cable Stayed Bridges," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 29, pp. 409-418 (1988).
39. 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).
40. 顧明，「中國橋樑之抗風研究」，海峽兩岸橋樑工程學術與實務研討會－論文集，徐耀賜主編 (1995)。
41. Bietry, J., Sacre, C. and Simiu, E., "Mean Wind Profiles and Changes of Terrain Roughness," Journal of the Structural Division, ASCE, 104, pp. 1585-1593 (1978).
42. Kaimal, J. C., "Spectrum Charactertics of Surface-Layer Turbulence," J. Royal Meteorol. Soc., 98, pp.563-589 (1972).
43. Davenport, A. G., "The Spectrum of Horizontal Gustiness Near the Ground in High Winds," J. Royal Meteorol Soc., 87, pp. 194-211 (1961).
44. Lumley, J. L. and Panofsky, H. A., The Structure of Atmospheric Turbulence, Wiley, New York (1964).
45. Davenport, A. G., "The Dependence of Wind Load upon Metrorological Parameters," Proceedings of the International Research Seminar on Wind Effects on Buildings and Structure, University of Toronto, pp. 19-82 (1968).
46. Vickery, B. J., "On the Reliability of Gust Loading Factors," Proceedings of the Technical Meeting Concerning Wind Loads on Buildings and Structures, National Bureau of Standards, Building Science Series 30, Washington, D.C., pp. 93-104 (1970).
47. Shiotani, M., "Structure of Gusts in High Winds, Part 1-4", The Physical Sciences Laboratory, Nikon University, Furabashi, Chiba, Japan (1967-1971).
48. Kristensen, L. and Jensen, N. O., "Lateral Coherance in Isotropic Turbulence and in the Natural Wind," Bound. Layer Meterol., 17, pp. 353-373 (1979).
49. Blackadar, A. K., Panofsky H. A. and Fiedler, F., Investigation of the Turbulent Wind Field Below 500 Feet Altitude at the Eastern Test Range, Florida, NASA CR-2438, National Aeronautics and Space Administration, Washington, D.C. (1974).
50. 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. 64-74 (1995).
51. Jones, A. J., Nicholas, P. and Scanlan, R. H. "Coupled Flutter and Buffeting Analysis of Long-Span Bridges," Journal of Structural Engineering , ASCE, Vol 122, No. 7, pp.716-pp.725 (1996)
52. Jones, A. J., Nicholas, P. and Scanlan, R. H., "Coupled Aeroelastic and Aerodynamic Response Analysis of Long-Span Bridges," Journal of Wind Engineering and Industrial Aerodynamics ,Vol 60 pp. 69-80 (1996).
53. Scanlan, R. H., "The Action of Flexible Bridges under Wind, Part I. (Flutter Theory)," Journal of Sound and Vibration, 60(2), pp. 187-199 (1978).
54. Matsumoto M., Kobayashi Y., Shirato H., "The influence of aerodynamic derivatives on flutter," Journal of Wind Engineering and Industrial Aerodynamics , Vol 60 pp.227-239 (1996).
55. Scanlan R.H., Jones N.P. , Singh L., "Inter-relations among flutter derivatives," Journal of Wind Engineering and Industrial Aerodynamics ,Vol 69-71 pp. 829-837 (1997)
56. Thorbek L.T., Hansen S.O., "Coupled buffeting response of suspension bridges," Journal of Wind Engineering and Industrial Aerodynamics ,Vol 74-76 pp. 839-847 (1998)
57. 李鳳娟，「振態耦合對大跨度橋樑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)。
58. 中華民國交通部台灣區國道新建工程局，「第二高速公路後續計劃：高屏溪橋細步設計」(1993)。
59. 中華民國交通部台灣區國道新建工程局，「第二高速公路後續計劃燕潮九如段：高屏溪橋（主橋）風洞試驗報告」（1994）。
60. 孫大衛，「複頻調質阻尼器對大度橋受風力擾動之制振分析」，私立淡江大學土木工程研究所碩士論文 (1997)。
61. Igusa, T. and Xu, K., "Vibration control using multiple tuned mass damper," Journal of Sound and Vibration, 175(4), pp. 491-503 (1994).
62. 蔡子文，「斜張橋受風力載重之動力分析」，私立淡江大學土木工程研究所碩士論文 (1994)。
63. 曾森裕，「施工中之大跨度橋樑顫振及亂流效應分析」，私立淡江大學土木工程研究所碩士論文 (1996)。
64. 張國俊，「應用TMD於氣動力耦合橋之制振分析」，私立淡江大學土木工程研究所碩士論文 (1997)。
65. 李宗豪，「應用TMD於長跨徑橋樑亂流效應之制振分析」，私立淡江大學土木工程研究所碩士論文 (1998)。