臺灣博碩士論文加值系統

由於橋樑施工技術的進步以及高強度材料的發展使得現代橋樑的設計及建造朝向長跨徑與細長斷面。由於這種型式橋樑的柔度較其他型式橋樑大，使得此種橋樑更易受風力的影響，需要一些裝置來控制其氣動力行為。在這些控制裝置中，調諧質量阻尼器(TMD)已被裝置於現存橋樑內，且證明可有效的控制風所造成的振動反應。
一般結構物裝置TMD受陣風之反應大多是在頻率域的範疇內進行分析，此分析無法考慮長跨徑橋樑的幾何非線性效應。本文是在時間域內進行動力分析，瞭解結構系統在非線性時，TMD對結構的影響。為了在分析中考慮非線性效應，利用目標頻譜與ARMA模式產生亂流效應的時間歷時風力。有限元素程式，包含梁-柱元素與纜索元素，用來模擬斜張橋與調諧質量阻尼器裝置，考慮橋面版及橋塔的P-Δ效應以及纜索的中垂效應。為了降低迭代次數及簡化分析，橋體自身擾動力之模擬，與無因次化頻率有關，是在一已知風速下，經由測量其中一個節點的波長，在一個或幾個週期內作頻率之修正。
由本文可知，在時間域內分析時，TMD在質量比1%即可有不錯的制振效果。當橋樑跨徑很長或橋樑受到高風速的風載重時，結構幾何非線性效應的影響是很顯著的，考慮TMD在結構非線性分析時也能有不錯的制振效果，但是效果較線性差。

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, they are more susceptible to wind excitation and need some devices to control the aerodynamic effects. Among these devices, tuned mass dampers (TMDs) have been installed in some existed bridges, and their performance is proven to be effective against wind-induced vibrations.
However, previous studies were performed in frequency domain and the geometrical nonlinearities of long-span bridges could not be taken into account. In this study, a time domain approach is then presented to investigate the effects of the structural nonlinearities on tuned mass damper's performance. For incorporating the nonlinear effects into this analysis, an autoregressive moving average approach is used to generate the real-time buffeting loads based on the target frequency spectra. A finite element library, consisting of beam-column elements and cable elements, is used to model the cable-stayed bridge and the tuned mass damper. The P-Δ effects of the decks and towers and the sag effects of the inclined cables are considered. To reduce the iterations and simplify the analysis, the self-excited forces, related to the reduced frequency, are updated every cycle or several cycles by measuring the wave length of a node at a given wind speed.
In this paper, the tuned mass dampers have good reduction ratio in the time domain analysis when the mass ratio is 0.01. The geometrical nonlinearity becomes significant while the bridge span is long and/or the bridge is under wind excitations at high wind velocities. The bridge with tuned mass dampers is effective on supressing bridge response with the structure nonlinear analysis, but the reduction ratio is less than the linear analysis.

中文摘要I
英文摘要II
目錄III
表目錄V
圖目錄VI
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 顫振與亂流效應之研究2
1-2.2 調諧質量阻尼器之研究3
1-2.2.1 單一調質阻尼器 ( Single TMD )4
1-2.2.2 複頻調質阻尼器 ( Multiple TMD )7
1-2.3 時間序列 ( Time Series ) 的模擬8
1-3 本文內容10
第二章 TMD應用於長跨徑橋樑之頻率域分析12
2-1 橋體外力介紹12
2-1.1 自身擾動力13
2-1.2 亂流擾動力（Buffeting force）14
2-2 調諧質量阻尼器之理論15
2-2.1 無阻尼結構─TMD系統15
2-2.2 有阻尼結構─TMD系統19
2-3 TMD對橋樑之制振理論分析20
2-3.1 雙TMD模型運動方程式21
2-3.2 轉換函數(Transfer function)之推導25
2-3.3 橋樑對亂流效應之位移反應27
2-3.4 橋樑位移反應之折減率28
第三章 TMD應用於長跨徑橋樑之時間域分析30
3-1 系統運動方程式之建立31
3-1.1 系統質量矩陣與勁度矩陣31
3-1.2 系統複合振態阻尼矩陣33
3-2 橋體所受之外力矩陣35
3-2.1 時間歷時風力之模擬37
3-2.1.1 自迴歸模式(AR)37
3-2.1.2自迴歸移動平均模式(ARMA)40
3-2.2 亂流擾動力分析流程40
3-2.3 自身擾動力分析流程43
3-3 斜張橋之非線性效應44
3-4 動力分析模式48
3-5 加入TMD後之動力分析流程51
第四章 實例分析與結果53
4-1 分析模型53
4-1.1 簡支橋樑之斷面性質與結構模式53
4-1.2 斜張橋之斷面性質與結構模式54
4-1.3 TMD之結構模式55
4-2 例題一(程式驗證)58
4-3 例題二(簡支橋)59
4-3.1 時間域與頻率域分析之比較59
4-3.2 TMD制振效果分析60
4-4 例題三(斜張橋)63
4-4.1 時間域與頻率域分析之比較63
4-4.2 結構為線性之TMD制振效果分析64
4-4.3 結構為非線性之TMD制振效果分析65
第五章 結論與建議67
5-1 結論67
5-2 建議69
附 表70
附 圖79
參 考 文 獻109

參 考 文 獻
1. Nobuto, Y. Fujino and M. Ito, “A Study on the Effectiveness of TMD to Suppress A Coupled Flutter of Bridge Deck,” Journal of JSCE, October, pp. 413-416(1988).
2. William W. S. Wei, Time Series Analysis, Univariate and Multivariate Methods, 1-64, 332-381.
3. P. D. Spanosand B. A. Zeldin, “Efficient Iterative Arma Approximation of Multivariate Random Processes for Structural Dynamics Applications,” Earthquake Engineering and Structural Dynamics, Vol. 25,497-507 (1996).
4. J. Maeda and M. Makino,“ Characteristics of Gusty Winds Simulate by an A.R.M.A. Model,” Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 427-436.
5. Tanaka, H., N. Yamamura and M. Tatsumi, "Coupled Mode Flutter Analysis using Flutter Derivatives," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 41-44, pp. 1279-1290 (1992).
6. Bucher, C. G. and Y. K. Lin, "Stochastic Stability of Bridges Considering Coupled Modes," Journal of Engineering Mechanics, Vol. 114, No. 12, pp. 2064-2067 (1988)。
7. Bucher, C. G. and Y. K. Lin, "Stochastic Stability of Bridges Considering Coupled Modes," Journal of Engineering Mechanics, Vol. 115, No. 2, pp. 384-400 (1989)。
8. 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)。
9. Honda, A., N. Shiraishi, M. Matsumoto, Y. Fuse, K. Sumi and N. Sasaki, "Aerodynamic Stability of Kansai International Airport Access Bridge," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp. 533-542 (1993).
10. Den Hartog, J. P. Mechanical Vibration, 4th ed. McGraw-Hill, New York, (1956).
11. G. Jacquot and D. H. Hoppe, "Optimal Random Vibration Absorbers," Journal of Engineering Mechanics Division, Vol. 99, pp. 612-616 (1973).
12. H. Wirsching and G. C. Campbell, "Minimal Structure Response under Random Excitation using the Vibration Absorber," Earthquake Engineering and Structural Dynamics, Vol. 2, pp. 303-312 (1974).
13. B. Warburton, "Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters," Earthquake Engineering and Structural Dynamics, Vol. 10, pp. 381-401 (1982).
14. Gu, M. and H. F. Xiang, "Optimization of TMD for Suppressing Buffeting Response of Long-spsn Bridges," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 41-44, pp. 1383-1392 (1992).
15. H. C. Tsai. and G. C. Lin, "Optimum Tuned-Mass Dampers for Minimizing Steady-State Response of Support-Excited and Damped Systems," Earthquake Engineering and Structural Dynamics, Vol. 22, pp. 957-973 (1993).
16. Gu M. , 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).
17. Ioi and K. Ikeda, "On the Dynamic Vibration Damped Absorber of the Vibration System," Bull. JSME, (1978) 64.
18. Gu, M. and C. C. Chang, W. Wu, H. F. Xiang, "Increase of Critical Flutter Wind Speed of Long-Span Bridges using Tuned Mass Dampers," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 73, pp. 111-123 (1998).
19. Igusa and K. Xu, "Wide Band-response Characteristics of Multiple Subsystems with High Modal Density," Proc. 2nd int. conf. stochastic structure dynamics. Florida, U.S.A. (1990).
20. T. Igusa, and K. Xu, "Vibration Control Using Multiple Tuned Mass Damper," Journal of Sound and Vibration, 175(4), pp. 491-503 (1994).
21. Yamaguchi and N. Harnpornchai, "Fundamental Characteristics of Multiple Tuned Mass Dampers for Suppressing Harmonically Forced Oscillations," Earthquake engineering and structure dynamics, Vol. 22, pp. 51-62 (1993).
22. M. Abe and Y. Fujino, "Dynamic Characterization of Multiple Tuned Mass Dampers and Some Design Formulas," Earthquake engineering and structure dynamics, Vol. 23, pp. 813-835 (1994).
23. A. Kawaguchi, A. Teramura and Y. omote, "Time History Response of a Tall Building with a Tuned Mass Damper under Wind Force," Journal of Wind Engineering and Industrial Aerodynamics, Vol. 41-44, pp. 1949-1960 (1992).
24. J. Lardies. Analysis of a Multivariate Autoregressive Process. Mechanical Systems and Signal Processing (1996) 10 (6), 747-761.
25. Scanlan, R. H. and J. J. Tomko, "Airfoil and Bridge Deck Flutter Derivatives," Journal of Engineering Mechanics Division, Vol. 97, pp. 1717-1737 (1971).
26. Simiu, E. and R. H. Scanlan, Wind Effects on Structures, John Wiley & Sons.(1986)
27. Scanlan, R H. and R. H. Gade, "Motion of Suspended Bridge Spans under Gusty Wind," Journal of the Structural Division, pp. 1867-1883 (1977).
28. Kazama, H. Yamada and T. Miyata, “Wind Resistant Design for Long Span Suspension Bridges”, Journal of Wind Engineering and Industrial Aerodynamics, No 54/55 pp. 64-74 (1995).
29. Anurag Jain ,Nicholas P. Jones and Robert H. Scanlan, “Coupled Flutter and Buffeting Analysis of Long-Span Bridges”,Journal of the Structural Engineering ,Vol 122, No. 7, pp.716-pp.725 (1996)
30. Anurag Jain, Nicholas P. Jones and Robert H. Scanlan, “Coupled Aeroleastic and Aerodynamic Response Analysis of Long-Span Bridges”, Journal of Wind Engineering and Industrial Aerodynamics, Vol 60 pp. 69-80 (1996).
31. J. E. Brock,”A Note On The Damped Vibration Absorber.”, Transactions of the American Society of Mechanical Engineers A, 284. (1946).
32. Clough, R.W. And Penzien, J., Dynamics of Structures, McGraw-Hill Inc., Second Edition, 1993.
33. 呂顏龍, "大跨度橋樑受風載重之非線性分析─時間序列模擬",私立淡江大學土木工程研究所碩士論文,(1999).
34. Kaimal, J. C., "Spectrum Charactertics of Surface-Layer Turblence," J.Royal Meteorol.Soc., 98, pp.563-589 (1972).
35. Davenport, A. G., "The Spectrum of Horizontal Gustiness Near the Ground in High Winds," J. Royal Meteorol Soc., 87, pp. 194-211 (1961).
36. Lumley, J. L. and H. A. Panofsky, The Structure of Atmospheric Turbulence, Wiley, New York (1964).
37. Nazmy, A.S. And Abdel-Ghaffar, A. M., " Three-Dimensional Nonlinear Static Analysis of Cable-Stayed Bridges,"International Journal of Computer & Structures, Vol. 34, No.2, pp.257-271.
38. 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).
39. 李宗豪, "應用TMD於長跨徑橋梁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)
40. Fleming, J.F., “Nonlinear Static Analysis of Cable-Stayed Bridges Structures”, International Journal of Computer & Structures, Vol. 10, pp.621-635 (1979).
41. Ernst, J.H.,“ Der E-Modul von Seilen unter Berucksiechtigung des Dimensional, Der Bauingenieur”, 40(2), 1965.