TMD與TLCD的發展已有一段時間，TMD的諧調質量是鋼球，它的重量夠重，可輕易達到高樓層結構物的諧調質量，而發揮減振效果，適合使用在長週期的高樓層結構物。但通常高樓層結構物的結構振動週期較大，若採用TMD則相對的擺長亦需較長，需佔用二至三層樓的樓地板面積，影響空間使用效率；而TLCD可以放置於屋頂層，與民生用水及消防水箱結合，不需額外空間。但TLCD的諧調質量是水，水的密度小，若應用在高樓層重量大的結構物上，需有相當大的體積方可達到其諧調質量，發揮減振效益，而影響其使用用途。
本文的目的係根據TMD及TLCD的發展，在TMD與TLCD之間研究另外一種可行的阻尼器，結合TMD與TLCD的優點，並排除其缺點。本文首先探討於二維運動的TLCD水中增加一可沿圓弧滾動之鋼柱，鋼柱在圓弧面上之滾動與TMD近似，且鋼柱在水中滾動時，可藉由水來提供鋼柱滾動的阻尼。本文建立鋼柱滾動、液體運動及單自由度結構系統等3個運動方程式，由傅立葉轉換將時間域轉換為頻率域，繼而探討其在不同頻率範圍內的減振效益，經與前人的研究成果比較，確實可發揮阻尼器減振效應，有效縮小TLCD阻尼器體積，並可應用在主動控制上。
接著，本文亦研究鋼球在水中三維方向沿圓弧面滾動的結果，發現其沿圓弧面滾動結果可達類似TMD鐘擺之減振效應，且水體可提供鋼球沿圓弧面鐘擺型來回滾動之阻尼。此種三維方向沿圓弧面滾動的阻尼器因不受擺長之限制，適合放置在結構物之上，藉由運動方程式的建立，將離散時間系統下的狀態空間方程式導入，計算時間域範圍內的各項包括結構位移、速度、加速度、吸收能量等響應變化，發現此種阻尼器確實可發揮減振效益，並可擺脫TMD擺長的限制。

TMD and TLCD have been developed for a long time. The tuned mass of TMD is steel ball. It is heavy enough to apply on a heavy structure’s tuned mass to mitigate earthquake vibration. TMD is suitable for use in a tall building with long natural period but need 2 or 3 floors to fit for the length of the pendulum and affect the efficient use of building space. However TLCD can be installed on the roof of building and combine with domestic water and fire water tank with no additional space. The tuned mass of TLCD is water. Its density is so small that the TLCD need a large volume and weight enough for use of vibration mitigation in a heavy structure or a tall building, then affect its intended use.
The purpose of this article is based on the development of TMD and TLCD to find another damper that combine the advantages of TMD and TLCD and exclude the disadvantages. First adding a steel rod rolling along the arc on a 2-dimensional movement TLCD is investigated. The steel rod rolling along the arc is similar to TMD and water can provide the damping effect when steel rolls. The 3 equations of motion of steel rolling, liquid movement and single degree of freedom are formatted in this article and Fourier transformation employed to transform displacement of structure between time domain and frequency domain. The curved-TMLCD in this article can mitigate earthquake vibration and reduce the volume of TLCD effectively by studying on the effect of vibration control on different frequency range and comparing with the former research, same as in active control.
Next, the result of the steel ball rolling on the 3-dimensional curved surface in water is studied in this article and find that the vibration mitigation effect is similar to TMD that water can provide the damping force when steel ball rolls. This damper is suitable for setting on the structure because of unlimited length of pendulum. By formatting the equations of motion of this rolling damper and calculating the effect of structural displacement, velocity, acceleration and energy absorption, this damper can bring into play the vibration mitigation effect and get rid of the pendulum length restrictions.

論文審定書 i
誌 謝 ii
摘 要 iii
Abstract iv
目 錄 vi
圖 次 ix
表 次 xvii
符號說明 xviii
第一章 緒論 1
1.1 諧調阻尼器的發展及限制 1
1.2 文獻回顧 3
1.3 論文架構 6
第二章 液柱阻尼器內含鋼柱圓弧滾動之運動方程式 8
2.1鋼柱在水中沿圓弧面小範圍滾動之運動方程式 9
2.2圓弧底部TLCD液體運動方程式 12
2.3單自由度結構系統及鋼柱於水中圓弧滾動之運動方程式 17
2.4頻率域下之位移、鋼柱滾動及液面高低之轉換方程式 19
2.5地盤反力與結構互制之內含鋼柱圓弧滾動TMLCD位移轉換方程式 28
第三章 數值分析成果及擬最佳化公式探討 32
3.1與以前研究分析成果之比較及探討 32
3.2內含鋼柱圓弧滾動諧調液柱阻尼器數值分析成果 40
3.3擬最佳化過程中R及Cp/L與位移轉換函數之關係 42
3.4建立擬最佳化比較與查對之圖形及公式 46
3.5 擬最佳化後之分析成果與比較 50
第四章 主動控制式內含鋼柱圓弧滾動之諧調液柱阻尼器 58
4.1內含鋼柱圓弧滾動諧調液柱阻尼器之主動控制方程式 58
4.2 離散時間下之狀態空間運動方程式 61
4.3 最佳主動控制設計 65
4.4 單自由度結構系統內置主動控制TMLCD 70
第五章 多方向鋼球水中滾動阻尼器之動力行為 77
5.1雙向鐘擺型曲面 78
5.2鋼球雙向鐘擺型滾動曲面的回復力 82
5.3鋼球在水中雙向圓弧曲面鐘擺型滾動的摩擦力及阻尼力 87
5.4雙向鋼球鐘擺型水中滾動之運動方程式 88
5.5雙向鋼球鐘擺型水中滾動在離散時間系統下之狀態方程式 89
5.6 雙向鋼球鐘擺型水中滾動之案例分析 96
第六章 結構加裝鋼球水中多方向圓弧滾動阻尼器 120
6.1 結構設置多方向鋼球水中滾動RPS型TMD之狀態空間方程式 121
6.2 結構設置多方向鋼球水中滾動RPS型TMD動力反應及最佳化參數 131
6.3 最佳化結果之設計參數分析及比較 135
第七章 結論 164
參考文獻 168
附錄 176

Ahadi P., Mohebbi M., and Shakeri K., Using Optimal Multiple Tuned Liquid Column Dampers for Mitigating the Seismic Response of Structures, ISRN Civil Engineering, vol. 2012, Article ID 592181, 6 pages, 2012. doi:10.5402/2012/592181.
Almaz´an J. L., De la Llera J. C., Inaudi J. A., L´opez-Garc´ıa D., Izquierdo L. E. (2007), A bidirectional and homogeneous tuned mass damper: A new device for passive control of vibrations, Engineering Structures, Volume 29, Issue 7, Pages 1548–1560.
Bakre S. V., Jangid R. S. (2007), Optimum parameters of tuned mass damper for damped main system, Structural Control and Health Monitoring, Volume 14, Issue 3, pages 448–470.
Balendra T., Wang C. M., Cheong H. F. (1995), Effectiveness of tuned liquid column dampers for vibration control of towers, Engineering Structures, Volume 17, Issue 9, pages 668-675.
Chakrabortya S.,Debbarmaa R., Maranob G. C. (2012), Performance of tuned liquid column dampers considering maximum liquid motion in seismic vibration control of structures, Journal of Sound and Vibration, Volume 331, Issue 7, pages 1519–1531.
Chang, C. C., Hsu, C. T. and Swei, S. M. (1998), Control of buildings using single and multiple tuned liquid column dampers, Structural Engineering and Mechanics, Volume 6, Number 1, pages 77-93.
Chen, Y. H. and Ko, C. H. (2003), Active Tuned Liquid Column Damper with Propellers, Earthquake Engineering and Structural Dynamics, Volume 32, Issue 10, pages 1627–1638.
Den Hartog J. P., Mechanical Vibrations. Courier Dover Publications, 1985.
Eröz M., DesRoches R. (2008), Bridge seismic response as a function of the Friction Pendulum System (FPS) modeling assumptions, Engineering Structures, Volume 30, Issue 11, pages 3204–3212.
Farshidianfar A. and Oliazadeh P. (2009), Closed form optimal solution of a tuned liquid column damper responding to earthquake, World Academy of Science, Engineering and Technology 59 2009.
Farshidianfar A. and Soheili S. (2011), Tuned liquid column dampers for earthquake oscillations of high-rise structures including soil-structure interaction, 19th Annual Conference on Mechanical Engineering-ISME2011.
Fu C. (2010), Application of torsional tuned liquid column gas damper for plan-asymmetric buildings, Structural Control and Health Monitoring, Volume 18, Issue 5, pages 492–509.
Fujino, Y. Pacheco, B. Chaiseri, P., and Sun, L., (1988), Parametric Studies on Tuned Liquid Damper (TLD) Using Circular Containers by Free-Oscillation Experimant, Structural Engineering / Earthquake Engineering, Volume 5, Number 2, pages 381s-391s.
Fujino, Y., Sun, L., Pacheco, B. and Chaiseri, P. (1992),Tuned Liquid Damper (TLD) for Suppressing Horizontal Motion of Structures, Journal of Engineering Mechanics, Volume 118, Issue 10, pages 2017-2030.
Fujino, Y. and Sun, L.M. (1993), Vibration Control by Multiple Tuned Liquid Dampers (MTLDs), Journal of Structural Engineering, Volume 119, Number 12, pages 3482-3502.
Fujino Y., Siringoringo D.M., Nagayama T. and Su D. (2010), Control, simulation and monitoring of bridge vibration – Japan’s recent development and practice, IABSE-JSCE Joint Conference on Advances in Bridge Engineering-II, August 8-10, 2010, Dhaka, Bangladesh.
Gao, H., Kwok, K. S. C. and Salami, B. (1999), Characteristics of multiple tuned liquid column dampers in suppressing structural vibration, Engineering Structures, Volume 21, Issue 4, pages 316–331.
Ghosh, A. and Basu, B. (2007), A closed-form optimal tuning criterion for TMD in damped structures, Structural Control and Health Monitoring, Volume 14, Issue 4, pages 681–692.
Ghosh, A. and Basu, B. (2005), Effect of soil interaction on the performance of liquid column dampers for seismic applications, Earthquake Engineering and Structural Dynamics. Volume 34, Issue 11, pages 1375–1389.
Ghosh, A. and Basu, B. (2004), Seismic vibration control of short period structures using the liquid column damper, Engineering Structures, Volume 26, Issue 13, Pages 1905–1913.
Ghosh, R. and Ghosh, A. (2008), Soil interaction effects on the performance of compliant liquid column damper for seismic vibration control of short period structures, Structural Engineering and Mechanics, Volume 28, Issue 1, pp.89-105.
Hadi M. N., and Arfiadi Y. (1998), Optimum design of absorber for MDOF structures, Journal of Structural Engineering, Volume 124, Issue 11, pages 1272-1280.
Hoang N., and Warnitchai P. (2005), Design of multiple tuned mass dampers by using a numerical optimizer, Earthquake Engineering and Structural Dynamics, Volume 34, Issue 2, pages 125–144.
Honda, S., Kagawa, K., Fujita, K. and T. Hibi (1992), Damping of Wind-Induced Vibration on Medium High Buildings, Summaries of Technical Papers in Annual Meeting, AIJ:1093-1094 (in Japanese).
Huo L. S., Li H. N. (2011), Seismic response reduction of eccentric structures using liquid dampers, Vibration Analysis and Control - New Trends and Developments, Dr. Francisco Beltran-Carbajal (Ed.), ISBN: 78-953-307-433-7, InTech, DOI:10.5772/24073.
Ito, T. (1991), Experimental Verification of Effectiveness of Mutiple Tuned Liquid Damper, BS thesis, University of Tokyo, Tokyo, Japan.
Kareem, A., Kijewski, T., Tamura, Y. (1999), Mitigation of Motions of Tall Buildings with Specific Examples of Recent Applications, Wind and Structures, Volumn 2, Number 3, pages 201-251.
Kareem, A., and W.-J. Sun. (1987), Stochastic Response of Structure with Fluid-Containing Appendages, Journal of Sound and Vibration, Volume 119, Issue 3, 22 December 1987, Pages 389–408.
Lee C. L., Chen Y. T., Chung L. L., and Wang Y. P. (2006), Optimal design theories and applications of tuned mass dampers, Engineering Structures, Volume 28, Issue 1, pages 43–53.
Lee, H.H. and Juang H.H. (2012), Experimental study on the vibration mitigation of offshore tension leg platform system with UWTLCD, Smart Structures and Systems, Volume 9, Issue ,1, pages 71-104.
Lee, H. H., Wong, S. H. and Lee, R. S. (2006), Response Mitigation on the Offshore Floating Platform System with Tuned Liquid Column Damper, Ocean Engineering, Volume 33, Issues 8–9, pages 1118–1142.
Legeza V. P. (2004), Dynamics of vibroprotection systems with a ball-type low-frequency oscillation absorber, Strength of materials, Volume 36, Issue 3, pages 282-290.
Legeza V. P. (2004), Dynamics of vibroprotective systems with roller dampers of low-frequency vibrations, Strength of materials, Volume 36, Issue 2, pages 185-194.
Legeza V. P. (2013), Efficiency of a vibroprotection system with an isochronous roller damper, Mechanics of Solids, Volume 48, Issue 2, pages 168-177.
Li H. N., Yi T. H., Jing Q. Y., Huo L. S., and Wang G. X. (2012), Wind-induced vibration control of Dalian International Trade Mansion by tuned liquid dampers, Hindawi Publishing Corporation Mathematical Problems in Engineering, Volume 2012, Article ID 848031, 21 pages.
Lu L. Y., Chung L. L., Wu L. Y., and Lin G. L. (2006), Dynamic analysis of structures with friction devices using discrete-time state-space formulation, Computer and Structures, Volume 84, Issues 15–16, pages 1049–1071.
Malekghasemi H., Mercan O. (2011), Experimental and analytical investigations of rectangular tuned liquid dampers (TLDs), Report of Centre for the Resilience of Critical Infrastructure, Department of Civil Engineering, University of Toronto.
Malekghasemi H. (2011), Experimental and analytical investigations of rectangular tuned liquid dampers (TLDs), Master of Applied Science Department of Civil Engineering, University of Toronto.
Matta E., Stefano A. D. and Spencer B. F. J. (2009), A new passive rolling-pendulum vibration absorber using a non-axial-symmetrical guide to achieve bidirectional tuning, Earthquake Engineering and Structural Dynamics, Volume 38, Issue 15, pages 1729–1750.
Min, K. W., Kim, H. S., Lee, S. H., Kim, H. and Ahn, S. K. (2005), Performance Evaluation of Tuned Liquid Column Dampers for Response Control of a 76-story Benchmark Building, Engineering Structures, Volume 27, Issue 7, pages 1101–1112.
Modi, V. J. and Welt F. (1987), Vibration control using nutation dampers, Proceedings of the International Conference on Flow Induced Vibrations, BHRA, London (1987), pages 369–376.
Nanda B. and Biswal K. C. (2011), Application of tuned liquid damper for controlling structural vibration due to earthquake excitations, Modern Methods and Advances in Structural Engineering and Construction, ISEC-6, Zürich, June 21–26.
Ok S. Y., Song J., and Park K. S. (2009), Development of optimal design formula for bi-tuned mass dampers using multi-objective optimization, Journal of sound and Vibration, Volume 322, Issues 1–2, pages 60–77.
Rabiei M. (2008), Effect of bearing characteristics on the response of friction pendulum base-isolated buildings under three components of earthquake excitation, 2008 NZSEE Conference.
Rüdinger F. (2007), Tuned mass damper with nonlinear viscous damping, Journal of Sound and Vibration, Volume 300, Issues 3–5, pages 932–948.
Sadek F., Mohraz M. and Lew H. S. (1998), Single- and multiple-tuned liquid column dampers for seismic applications, Earthquake Engineering and Structural Dynamics, Volume 27, Issue 5, pages 439–463.
Sadek F., Mohraz B., Taylor A. W. and Chung R. M. (1997), A method of estimating the parameters of tuned mass dampers for seismic applications, Earthquake Engineering and Structural Dynamics, Volume 26, Issue 6, pages 617–635.
Sakai F., Takaeda S., Tamaki T. (1989), Tuned Liquid Column Damper – New Type Device for Suppression of Building Vibrations, Proceedings of International Conference on High Rise Buildings, Najing, China, pages 926–931.
Sakai F., Takaeda S. and Tamaki T. (1991), Tuned Liquid Column Dampers (TLCD) for Cable-Stayed Bridges, Proceedings Specialty Conference Innovation in Cable-Stayed Bridges, Fukuoka, JSCE, Japan, pages 197-205.
Saoka Y., Sakai F., Takaeda S. and Tamaki T. (1988), On the Suppression of Vibrations by Tuned Liquid Column Dampers, Annual Meeting of JSCE, Japan, Tokyo, 1988.
Won A. Y. J., Pires J. A. and Haroun M. A. (1996), Stochastic seismic performance evaluation of tuned liquid column dampers, Earthquake Engineering and Structural Dynamics, Volume 25, Issue 11, pages 1259–1274.
Xu, Y. L. and Shum, K. M. (2003), Multiple-tuned liquid column dampers for torsional vibration control of structures : theoretical investigation, Earthquake Engineering and Structural Dynamics, Volume 32, Issue 2, pages 309–328.
Xu, Y. L., Samali, B. and Kwok, K. C. S. (1992), Control of along – Wind response of the structures by mass and liquid dampers, Journal of Engineering Mechanics, ASCE, Volume 118, Issue 1, pages 20-39.
Yalla, S. K., Kareem, A. and Kantor, J. C. (2001), Semi-active Tuned Liquid Column Dampers for Vibration Control of Structures, Engineering Structures, Volume 23, pages 1469-1479.
Yalla, S. K. and Kareem, A. (2003), Semi-active Tuned Liquid Column Dampers Experimental Study, Journal of Structural Engineering, Volume 129, Issue 7, pages 960–971.
Yoneda M., Fujino Y., Kande H., Yamamoto A., Miyamoto Y., Ando O., Maeda K. and Katayama T. (1989), A practical study of tuned liquid damper with application to the sakitama bridge, Journal of Wind Engineering, Volume 41, pages 105-106.
吳賴雲、鍾立來、張忠信、黃旭輝、陳家乾 (2008)，非線性調諧質塊阻尼器設計參數最佳化之研究，中華民國結構工程學會，結構工程期刊，第23卷，第2期，第107-136頁。
鍾立來、吳賴雲、林廷翰、林美君、連冠華 (2009)，雙向摩擦鐘擺型調諧質塊阻尼器減震效益之研究，國家地震工程研究中心報告，NCREE-09-024。
鍾立來、吳賴雲、陳宣宏、黃旭輝、張忠信、林廷翰 (2008)，摩擦鐘擺型調諧質塊阻尼器之最佳化設計研究，國家地震工程研究中心報告，NCREE-08-018。