Title

應用相位控制於被動及半主動調諧質塊阻尼器之耐震設計

Translated Titles

Application of Phase Control for Seismic Design of Passive and Semi-active Tuned Mass Dampers

DOI

10.6342/NTU.2012.02285

Authors

顧丁與

Key Words

調諧質塊阻尼器 ; 基底振動 ; 最佳化設計 ; 相位控制原理 ; 半主動控制 ; tuned mass damper ; base vibration ; optimal design ; principle of phase control ; semi-active control

PublicationName

臺灣大學土木工程學研究所學位論文

Volume or Term/Year and Month of Publication

2012年

Academic Degree Category

碩士

Advisor

吳賴雲;鍾立來

Content Language

繁體中文

Chinese Abstract

本文旨在探討於線性被動式調諧質塊阻尼器 (Tuned Mass Damper, TMD) 之最佳化設計,以及相位控制之控制律 (control algorithm) 於半主動式TMD受基底振動下之減振效益的研究。首先,以單自由度系統加裝一線性被動式TMD,在白雜訊 (white noise) 基底加速度作用下,分別推導其結構位移及絕對加速度均方 (mean square) 最小化,使用迭代法及設計公式等兩種方式,提出線性被動式TMD之參數最佳化設計方法。接著,以相位控制為控制原理,提出一組控制律,欲使半主動式TMD之相對位移與結構位移保持 -90度的相位差。隨後以一週期為3秒之單自由度結構,分別受正弦波與隨機基底加速度作數值模擬,其結果顯示結構加裝TMD後,可有效降低結構整體反應,加裝半主動式TMD可較加裝被動式TMD有更大之減振頻率帶寬,且由頻率比敏感度及TMD阻尼比敏感度分析,半主動式TMD有較好的適應性,不需額外的阻尼;而經由三維圖搜尋半主動式TMD之最佳設計值頻率比與直接取TMD之頻率等於結構第一振態之頻率進行比較,其減振效果差異不大,有著很好的強健性。最後以兩個實際地震歷時進行數值模擬,分別為東西向El Centro地震及300%東西向花蓮331地震,其分析結果顯示,無論是被動式TMD或半主動式TMD,對於降低結構極值之效果皆屬不佳,但半主動式TMD仍對其設計參數不敏感,且相較於被動式TMD,有著更佳的整體減振效果;同樣以三維圖尋找半主動式TMD之最佳設計值頻率比與直接取TMD之頻率等於結構第一振態之頻率進行比較,其減振效果亦差異不大,可不需進行最佳化設計,即可有不錯的減振效果。由上述之模擬,可驗證以此控制律作用之半主動式TMD確實有效並有其優點。

English Abstract

The vibration suppression effect under base excition is proposed in this study that the optimal design for linear passive tuned mass damper (PTMD) and control algorithm of phase control for semi-active tuned mass damper (SATMD). Firstly, a linear tuned mass damper is installed on a single-degree-of-freedom (SDOF) system. The minimum mean square of structural displacement and absolute acceleration can be derived respectively under the white noise base acceleration. So the two methods of optimal parameters design for linear PTMD are proposed by using the iteration method and the design formula. Then making use of the phase control as the control principle, the control algorithm can be proposed. It makes the relative displacement of SATMD maintain 90 degree lag to the structural displacement. The SDOF structure with a period of 3 seconds is subjected to sinusoidal and random base acceleration, respectively. The results of numerical simulations show that after installing TMD, the structural response can be reduced effectively. To compare the effective frequency range of vibration suppression, SATMD is wider than PTMD. In addition, the sensitivity analyses of frequency ratio and TMD damping ratio, respectively, show that SATMD has better adaptability than PTMD and needs no additional damper. Searching through the three-dimensional figure of structural response with frequency ratio and TMD damping ratio can find that the mininmum structural response is little different to the structural response with frequency ratio equals to one. It means that the SATMD a good robustness. Finally, the numerical simulations of two earthquake excitations show some results. Whether the TMD is passive or semi-active, it is not good for reducing the peak value of structural response. However, SATMD is still not sensitive to the parameters and has more effective vibration suppression than PTMD on the whole. Searching through the three-dimensional figure can also find that the mininmum structural response is little different to the structural response with frequency ratio of SATMD equals to one. The SATMD may not need to use the optimal design, and it can have good vibration suppression effect. By the above numerical simulation, it can be verified that the SATMD by using the proposed control algorithm is indeed valid and has its advantages.

Topic Category 工學院 > 土木工程學研究所
工程學 > 土木與建築工程
Reference
  1. [2] Spencer, Jr. B.F. and Soong T.T., “New Applications and Development of Active, Semi-active and Hybrid Control Techniques for Seismic and Non-Seismic Vibration in the USA”. Proceedings of International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibration of Structures, Cheju, Korea, August 23-25, 1999.
    連結:
  2. [4] Miyashita K., Itoh M., Fujii K., Yamashita J., and Takahashi T., “Full-scale Measurements of Wind-induced Responses on the Hamamatsu ACT Tower”. Journal of Wind Engineering and Industrial Aerodynamics, Elsevier Science, 74-76: 943-953, 1998.
    連結:
  3. [7] Den Hartog J.P., Mechanical Vibrations, 4th Edition, McGraw-Hill, New York, 1956.
    連結:
  4. [8] Ioi T. and Ikeda K., “On the Dynamic Vibration Damped Absorber of the Vibration System”. Bulletin of the Japanese Society of Mechanical Engineering, 21(151): 64-71, 1978.
    連結:
  5. [9] Warburton G.B. and Ayorinde E.O., “Optimum absorber parameters for simple systems”. Earthquake Engineering and Structural Dynamics, 8: 197-217, 1980.
    連結:
  6. [10] Ayorinde E.O. and Warburton G.B., “Minimizing structural vibrations with absorbers”. Earthquake Engineering and Structural Dynamics, 8: 219-236, 1980.
    連結:
  7. [11] Warburton G.B., “Optimum absorber parameters for various combinations of response and excitation parameters”. Earthquake Engineering and Structural Dynamics, 10: 381-401, 1982.
    連結:
  8. [12] Tsai H.C. and Lin G.C., “Optimum tuned mass dampers for minimizing steady-state response of support excited and damped systems”. Earthq. Engng Struct. Dynam, 22: 957-973, 1993.
    連結:
  9. [13] Sadek F., Mohraz B., Taylor A.W., and Chung R.M., “A method of estimating the parameters of mass dampers for seismic applications”. Earthquake Engineering and Structural Dynamics, 26: 617-635, 1997.
    連結:
  10. [14] Bakre S.V. and Jangid R.S., “Optimum parameters of tuned mass damper for damped main system”. Structural Control and Health Monitoring, 14: 448-470, 2007.
    連結:
  11. [15] Asami T. and Nishihara O., “Closed-form exact solution to H-infinity optimization of dynamic vibration absorbers (Application to different transfer functions and damping systems)”. Journal of Vibration and Acoustics-Transactions of the Asme, 125(3): 398-405, 2003.
    連結:
  12. [16] Kaynia A. M., Biggs J. M., and Veneziano D., “Seismic Effectiveness of Tuned Mass Dampers”. Journal of the Structural Division, Vol. 107, No. 8: 1465-1484, 1981.
    連結:
  13. [17] Sladek J. R. and Klingner R. E., “Effect of Tuned-Mass Dampers on Seismic Response”. Journal of Structural Engineering, Vol. 109, No. 8: 2004-2009, 1983.
    連結:
  14. [18] Soto R. and Ruiz SE., “Influence of ground motion intensity on the effectiveness of tuned mass dampers”. Earthquake Engineering and Structural Dynamics, 28: 1255-1271, 1999.
    連結:
  15. [19] Pinkaew T., Lukkunaprasit P., and Chatupote P., “Seismic effectiveness of tuned mass dampers for damage reduction of structures”. Engineering Structures, Vol. 25: 39-46, 2003.
    連結:
  16. [20] Chung L.L., Wu L.Y., Yang C.S., and Lien K.H., “Optimal design formulas for viscous tuned mass dampers in wind-excited structures”. Structural Control and Health Monitoring, DOI: 10.1002/stc.496, 2011.
    連結:
  17. [21] Chang J. C. H. and Soong T. T., “Structural Control Using Active Tuned Mass Dampers”. Journal of Engineering Mechanics, Vol. 106: 1091-1098, 1980.
    連結:
  18. [23] Huang K. M. and Chou T. J., “Use of Active Mass Dampers for Wind and Seismic Control on Super-high-rise Buildings”. The Structural Design of Tall Buildings, Vol. 4: 27-45, 1995.
    連結:
  19. [24] Nagashima I., “Optimal displacement feedback control law for active tuned mass damper”. Earthquake Engineering and Structural Dynamics, 30: 1221-1242, 2001.
    連結:
  20. [25] Li C., “Multiple active–passive tuned mass dampers for structures under the ground acceleration”. Earthquake Engineering and Structural Dynamics, Vol. 32: 949-964, 2003.
    連結:
  21. [26] Samali B. and Al-Dawod M., “Performance of a five-storey benchmark model using an active tuned mass damper and a fuzzy controller”. Engineering structures, Vol. 25: 1597-1610, 2003.
    連結:
  22. [27] Li C. and Qu W., “Evaluation of elastically linked dashpot based active multiple tuned mass dampers for structures under ground acceleration”. Engineering structures, Vol. 26: 2149-2160, 2004.
    連結:
  23. [28] Guclu R. and Yazici H., “Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers”. Journal of Sound and Vibration, Vol. 318: 36-49, 2008.
    連結:
  24. [30] Hrovat D., Barak P., and Rabins M., “Semi‐Active Versus Passive or Active Tuned Mass Dampers for Structural Control”. Journal of Engineering Mechanics. Vol. 109: 691-701, 1983.
    連結:
  25. [31] Abe M. and Igusa T., “Semi-active dynamic vibration absorbers for controlling transient response”. Journal of Sound and Vibration, Vol. 198: 547-569, 1996.
    連結:
  26. [32] Abe M., “Semi-active tuned mass dampers for seismic protection of civil structures”. Earthquake Engineering and Structural Dynamics, Vol. 25: 743-749, 1996.
    連結:
  27. [33] Pinkaew T. and Fujino Y., “Effectiveness of semi-active tuned mass dampers under harmonic excitation”. Engineering Structures, Vol. 23: 850-856, 2001.
    連結:
  28. [34] Aldemir U., “Optimal control of structures with semiactive-tuned mass dampers”. Journal of Sound and Vibration, Vol. 226: 847-874, 2003.
    連結:
  29. [35] Lin P. Y., Chung L. L. and Loh C. H., “Semiactive control of building structures with semiactive tuned mass damper”. Computer-Aided Civil and Infrastructure Engineering, Vol. 20: 35-51, 2005.
    連結:
  30. [36] Lin C. C., Lin G. L. and Wang J. F., “Protection of seismic structures using semi-active friction TMD”. Earthquake Engineering and Structural Dynamics, Vol. 39: 635-659, 2010.
    連結:
  31. [37] Lin C.C., Lu L.Y., Lin G. L. and Yang T.W., “Vibration control of seismic structures using semi-active friction multiple tuned mass dampers”. Engineering Structures, Vol. 32: 3404-3417, 2010.
    連結:
  32. [38] Kang J., Kim H. S., and Lee D. G., “Mitigation of wind response of a tall building using semi-active tuned mass dampers”. John Wiley & Sons, 2010.
    連結:
  33. [39] 鍾立來、吳賴雲、賴勇安、連冠華、顧丁與,「應用相位控制原理於調諧質塊阻尼器最佳化結構控制設計」,國家地震工程研究中心,報告編號:NCREE-11-024,2011。
    連結:
  34. [40] Setareh M., “Application of semi-active tuned mass dampers to base-excited systems”. Earthquake Engineering and Structural Dynamics, Vol. 30: 449-462, 2001.
    連結:
  35. [41] Setareh M., “Floor vibration control using semi-active tuned mass dampers”. Canadian Journal of Civil Engineering, Vol. 29: 76-84, 2002.
    連結:
  36. [43] Gu M., Chen S.R., and Chang C.C., “Control of wind-induced vibrations of long-span bridges by semi-active lever-type TMD”. Journal of Wind Engineering and Industrial Aerodynamics, Vol. 90: 111-126, 2002.
    連結:
  37. [44] Varadarajan N. and Nagarajaiah S., “Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/ hilbert transform”. Journal of engineering mechanics, Vol. 130: 451-458, 2004.
    連結:
  38. [45] Nagarajaiah S. and Varadarajan N., “Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD”. Engineering structures, Vol. 27: 431-441, 2005.
    連結:
  39. [46] Nagarajaiah S. and Sonmez E., “Structures with Semiactive Variable Stiffness Single Multiple Tuned Mass Dampers”. Journal of Structural Engineering, Vol.133: 67-77, 2007.
    連結:
  40. [47] Collins R., Basu B., and Broderick B., “Bang-bang and semiactive control with variable stiffness TMDs”. Journal of Structural Engineering, Vol.134: 310-317, 2008.
    連結:
  41. [48] Lourenco R., Roffel A. J., and Narasimhan S., “Adaptive Pendulum Mass Damper for the Control of Structural Vibrations”. Cansmart 2009 International Workshop SMART MATERIALS AND STRUCTURES, 17-26, Montreal, Quebec, Canada, 2009.
    連結:
  42. [49] Roffel A.J., Lourenco R., Narasimhan S., and Yarusevych S. “Adaptive Compensation for Detuning in Pendulum Tuned Mass Dampers”. Journal of Structural Engineering, Vol.137: 242-251, 2010.
    連結:
  43. [51] Nagarajaiah S. and Pasala D. T. R., “NEESR-Adapt-Struct: Semi-active control of ASD Device—Adaptive Length Pendulum Dampers”. 19th Analysis & Computation Specialty Conference, ASCE, 325-334, 2010.
    連結:
  44. [52] Newland D.E. An Introduction to Random Vibrations Spectral and Wavelet Analysis, 3rd Edition, Longman Scientific and Technical, New York, 1993.
    連結:
  45. [54] Soong T. T. and Dargush G. F. Passive Energy Dissipation Systems in Structural Engineering. Wiley, New York, 1997.
    連結:
  46. [55] 鍾立來、吳賴雲、賴勇安、連冠華、黃旭輝,「以結構位移均方最小化作調諧質塊阻尼器之最佳設計」,結構工程,第二十六卷,第四期,第31-58頁,2011。
    連結:
  47. [1] 內政部營建署,「建築物耐震設計規範及解說」,中華民國,2011。
  48. [3] Chu S.Y., Soong T.T., and Reinhorn A.M., “Active, Hybrid and Semi-Active Structural Control”. Wiley, New York, 2005.
  49. [5] Frahm H., “Device for Damped Vibrations of Bodies”. Patent No.989958, U. S., 1909.
  50. [6] Ormondroyd J. and Den Hartog J.P., “The theory of dynamic vibration absorber”. Trans, ASME, APM-50-7: 9-22, 1928.
  51. [22] Aizawa S., Fukao Y., Minewaki S., Hayamizu Y., Abe H. and Haniuda N., “An experimental study on the active mass damper”. Proceedings of Ninth World Conference on Earthquake Engineering, Vol. 5: 871-876, 1988.
  52. [29] 鍾立來、吳賴雲、李明璆、楊培堅,「東帝士85國際廣場之結構主動控制」,結構工程,第十四卷,第二期,第45-65頁,1999。
  53. [42] Setareh M., Ritchey J.K., Murray T.M., Koo J.H. and Ahmadian M., “Semiactive Tuned Mass Damper for Floor Vibration Control”. Journal of Structural Engineering, Vol.133: 242-250, 2007.
  54. [50] Nagarajaiah S, Pasala D. T. R, and Huang C., “Smart TMD: adaptive length pendulum dampers”. Proceedings 5th World Conference on Structural Control and Monitoring, Number: 275, Tokyo, 2010.
  55. [53] 洪維恩,「Matlab 7 設計程式」,旗標出版公司,1993。