隨著隔震技術日趨成熟，今日已有許多建築與橋樑藉由安裝滑動式隔震元件以提升其耐震能力，但現行採用較多之滑動隔震支承屬於傳統定曲率之摩擦單擺支承，其於近斷層或長週期震波作用下易產生似共振現象之缺點，為確保隔震系統之安全性，因此有單擺式變曲率滑動隔震支承 (sliding isolator with various curvature，SIVC)及雙擺變曲率滑動隔震支承(double sliding isolator with various curvature，DSIVC)之研發。目前有關SIVC 與DSIVC 的研發多侷限於理論研究或小承載力的實驗研究，若要將之應用至實際隔震結構，放大摩擦子尺寸以增加支承承載能力為必然之趨勢。因此，如何於變曲率支承分析中考慮摩擦子之尺寸效應為本文之研究重點。再者，隔震支承摩擦力模擬方法目前分為剪力平衡方法與文氏摩擦模型(Bouc-Wen friction model)，其中文氏模型對於設置多個隔震元件之大型結構分析較為適用，但目前尚缺乏以實驗驗證文氏模型模擬變曲率隔震支承摩擦力可行性之相關文獻。
有鑑於此，本文乃進行大尺度 SIVC 與DSIVC 支承單向元件測試，以驗證本文所提出之變曲率隔震支承分析理論與數值方法，該分析方法結合文氏摩擦模型並可考慮摩擦子尺寸效應對支承回復力之影響，本文稱之割線回復力理論。本研究更近一步利用前人之實驗資料驗證該理論用於模擬SIVC 與DSIVC 支承於雙向運動時之行為。實驗研究發現，使用楊氏係數較高之摩擦材料時，本文提出之割線回復力理論較能精確模擬支承曲率變化較劇烈之硬化段或曲率函數轉換處之遲滯行為。另則，研究亦發現於單擺與對稱雙擺之理論分析，文氏摩擦模型之數值穩定性較剪力平衡法佳，實驗資料則顯示此法可與本文割線回復力分析法結合，精確模擬SIVC 與DSIVC 支承於雙向運動中之摩擦力耦合行為，為可行之變曲率支承摩擦力數值模擬方法。

Due to the feature of variable curvature, the sliding isolators with variable curvature (SIVCs) is able to prevent excessive isolation displacement in a near-fault earthquake.However, most of current research results about SIVC are only applicable to light-weight structures or equipment, since they assumed the SIVC slider as a particle. If a SIVC is to be used in buildings or cases of high axial load, the slider has to be enlarged, so the slider size effect must be considered. To this end, this thesis establishes an analysis method for the large-scale SIVC with the consideration of the slider size effect.The method is applicable to a SIVC under uni- or bi-directional horizontal excitation. To experimental verify the analysis method, unidirectional cyclic element tests for large-scale single and double SIVC were conducted in this study. Comparison between experimental and theoretical results demonstrates that the hysteresis loops simulated by the proposed analysis method are more accurate than the results predicted by the conventional method neglecting slider size effect, particularly for isolator displacement around the sliding surface with higher curvature variation.

1. Becker T. C., Mahin S. A. (2012) “Experimental and analytical study of the bidirectional behavior of the triple friction pendulum isolator.” Earthquake Engineering & Structural Dynamics, 41: 355–373.
2. Bhayani, V. M., Panchal, V. R. (2018) “Seismic Response of Building-Equipment Isolated with Polynomial Friction Pendulum Isolator.” International Journal of Scientific Research in Science, Engineering and Technology, 4(5): 234–238.
3. Bouc, R. (1971) “Modele mathematique d'hysteresis.” Acustica, 24(1): 16–25.
4. Charalampakis, A. E., Koumousis, V. K. (2010) “Parameters of Bouc–Wen model revisited.” 9th HSTAM International Congress on Mechanics Limassol, Cyprus, July 12–14.
5. Constantinou, M. C., Adnane, M. A. (1987) “Dynamics of soil-based-isolated structure systems: Evaluation of two models for yielding systems.” Report to the National Science Foundation, Dept. of Civ. Engrg., Drexel Univ., Philadelphia, Pa.
6. Constantinou, M. C., Mokha, A., Reinhorn, A. (1990) “Teflon bearings in base isolation,part II: modeling.” ASCE Journal of Structural Engineering, 116(2): 455–474.
7. De Domenico, D., Ricciardi, G., Infanti, S. , Benzoni, G. (2019) “Frictional Heating in Double Curved Surface Sliders and Its Effects on the Hysteretic Behavior : An Experimental Study.” Frontiers in Built Environment, 5: 1–11.
8. Dhankot, M. A., Soni, D. P. (2017) “Behaviour of Triple Friction Pendulum Isolator under Forward Directivity and Fling Step Effect.” KSCE Journal of Civil Engineering,21(3): 872–881.
9. Fenz, D. M., Constantinou, M. C. (2006) “Behaviour of the double concave Friction Pendulum bearing.” Earthquake Engineering and Structural Dynamics, 35: 1403–1424.
10. Fenz D. M., Constantinou M. C. (2008a) “Spherical sliding isolation bearings with adaptive behavior: Theory.” Earthquake Engineering & Structural Dynamics, 37: 163–183.
11. Fenz D. M., Constantinou M. C. (2008b) “Spherical sliding isolation bearings with adaptive behavior: Experimental verification.” Earthquake Engineering and Structural Dynamics, 37: 185–205.
12. Fenz D. M., Constantinou M. C. (2008c) “Modeling Triple Friction Pendulum Bearings for Response-History Analysis.” Earthquake Spectra, 24(4): 1011–1028.
13. Han, Q., Liang, X., Wen, J., Zhang, J., Du, X., Wang, Z. (2020) “Multiple-variable frequency pendulum isolator with high-performance materials.” Smart Materials and Structures, 29(7): 1–13.
14. Jangid, R. S. (2005) “Computational numerical models for seismic response of structures isolated by sliding systems.” StructuralControl and Health Monitoring, 12: 117–137.
15. Khoshnoudian, F., Hemmati, T A. (2014) “Impact of structures with double concave friction pendulum bearings on adjacent structures.” Structures and Buildings, 167: 41–53.
16. Kim Y. S., Yun C. B. (2007) “Seismic response characteristics of bridges using double concave friction pendulum bearings with tri-linear behavior.” Engineering Structures, 29: 3082–3093.
17. Krishnamoorthy, A. (2015) “Seismic Control of Continuous Bridges Using Variable Radius Friction Pendulum Systems and Viscous Fluid Dampers.” International Journal of Acoustics and Vibration, 20(1): 24–35.
18. Lin, S. C., Han, J. Q, Zhao, H. T (2020) “Experimental and Theoretical Studies of Bidirectional Variable Curvature Friction Pendulum Bearing.” KSCE Journal of Civil Engineering, 24(5): 1568–1580.
19. Lu L. Y., Lee T. Y., Yeh S. W. (2011) “Theory and experimental study for sliding isolators with variable curvature.” Earthquake Engineering & Structural Dynamics, 40:1609–1627.
20. Lu L. Y., Lee T. Y., Juang S. Y. , Yeh S. W. (2013) “Polynomial friction pendulum isolators (PFPIs) for building floor isolation: An experimental and theoretical study.” Engineering Structures, 56: 970–982.
21. Ma, F., Zhang, H., Bockstedte, A., Foliente, G. C., Paevere, P. (2004) “Parameter analysis of the differential model of hysteresis.” Journal of Applied Mechanics, 71: 342–349.
22. Marin-Artieda, C. C., Whittaker, A. S., Constantinou, M. C. (2007) “Experimental and analytical study of the XY-friction pendulum (XY-FP) bearing for bridge applications.” Technical Report MCEER-07-0009, National Multidisciplinary and Multi-hazard Earthquake Engineering Research Center.
23. Marin-Artieda, C. C., Whittaker, A. S., Constantinou, M. C. (2009) “Experimental study of the XY-friction pendulum bearing for bridge applications.” ASCE Journal of Bridge Engineering, 14(3): 193–202.
24. Marin-Artieda, C. C., Whittaker, A. S. (2010) “Theoretical studies of the XY-FP seismic isolation bearing for bridges.” ASCE Journal of Bridge Engineering, 15(6): 631–638.
25. Meirovitch, L. (1990) Dynamics and Control of Structures, John Wiley & Sons,Inc.
26. Mokha, A. S., Constantinou, M. C., Reinhorn, A. M. (1990) “Teflon bearing in base isolation. I. testing.” ASCE Journal of Structural Engineering, 116(2): 438–454.
27. Murnal, P., Sinha, R. (2002) “Earthquake Resistant Design of Structures using the Variable Frequency Pendulum Isolator.” Journal of Structural Engineering, 128(7):870–880.
28. Panchal, V. R., Jangid, R. S., Soni, D. P., Mistry B. B. (2010) “Response of the double variable frequency pendulum isolator under triaxial ground excitations.” Journal of Earthquake Engineering, 14: 527–558.
29. Rabiei, M. (2008) “Effects of vertical ground motions on the seismic response of isolated structures with XY-Friction Pendulum system.” The 14th World Conference on
Earthquake Engineering, Beijing, China, October 12–17.
30. Rabiei, M., Khoshnoudian, F. (2013) “Seismic response of elevated liquid storage tanks using double concave friction pendulum bearings with tri-linear behavior.” Advances in Structural Engineering, 16(2): 315–337.
31. Roussis, P. C., Constantinou, M. C. (2006a) “Uplift-restraining Friction Pendulum seismic isolation system.”Earthquake Engineering and Structural Dynamics, 35: 577–593.
32. Roussis, P. C., Constantinou, M. C (2006b) “Experimental and analytical studies of structures seismically isolated with an uplift-restraining friction pendulum system.” Earthquake Engineering and Structural Dynamics, 35: 595–611.
33. Roussis, P. C. (2009) “Study on the effect of uplift-restraint on the seismic response of base-isolated structures.” ASCE Journal of Structural Engineering, 135(12): 1462–1471.
34. Sarlis, A. A., Constantinou, M. C. (2016) “A model of triple friction pendulum bearing for general geometric and frictional parameters.” Earthquake Engineering and Structural Dynamics, 45: 1837–1853.
35. Shahbazi, P., Moeindarbari, H., Taghikhany, T. (2013) “Comparative study on behavior of double variable curvature friction pendulum systems.” 13th World Conference on Seismic Isolation, Sendai, Japan, September 24–27.
36. Shahbazi, P., Taghikhany, T. (2014) “Comparative study on behavior of variable curvature friction pendulum isolator.” Second European Conference on Earthquake Engineering and Seismology, Istanbul, August 25–29.
37. Sharma, A. and Jangid, R. S. (2012) “Performance of variable curvature sliding isolators in base-isolated benchmark building.” The Structural Design of Tall and Special Buildings, 21: 354–373.
38. Sodha, A., Vasanwala, S. A., Soni, D. (2019) “Probabilistic evaluation of seismically isolated building using quintuple friction pendulum isolator.” Innovations in Infrastructure, Advances in Intelligent Systems and Computing, 757: 149–159.
39. Sodha, A., Vasanwala, S., Soni, D., Kumar, S., Kanan, T. (2020a) “Analytical study of triple friction pendulum under a different hazard level of earthquakes.” Advances in Structural Engineering and Rehabilitation, Lecture Notes in Civil Engineering, 38: 105–111.
40. Sodha, A., Vasanwala, S., Soni, D. (2020b) “Seismic response of structure isolated with quintuple friction pendulum bearing under directivity focusing earthquakes.” Advances in Computer Methods and Geomechanics, Lecture Notes in Civil Engineering, 55: 629–637.
41. Soni, D. P., Mistry, B. B., Panchal, V. R. (2010) “Behaviour of asymmetric building with double variable frequency pendulum isolator.” Structural Engineering and Mechanics,34(1): 61–84.
42. Soni, D. P., Mistry, B. B., Jangid, R. S., Panchal, V. R. (2011a) “Seismic response of the double variable frequency pendulum isolator.” Structural Control and Health Monitoring, 18: 450–470.
43. Soni, D. P., Mistry, B. B., Panchal, V. R. (2011b) “Double variable frequency pendulum isolator for seismic isolation of liquid storage tanks.” Nuclear Engineering and Design, 241: 700–713.
44. Soni, D. P., Mistry, B. B., Panchal, V. R. (2012) “ Seismic isolation of bridges with double variable frequency pendulum isolator.” Advances in Structural Engineering, 15(2): 185–203.
45. Tsai, C. S., Chiang, T.,C., Chen, B. J. (2003) “Finite element formulations and theoretical study for variable curvature friction pendulum system.” Engineering Structures, 25:1719–1730.
46. Wang, L. W., Lu, L. Y. (2018) “Generic 3D formulation for sliding isolators with variable curvature and its experimental verification.” Engineering Structures, 177: 12–29.
47. Wen, Y. K. (1976) “Method for random vibration of hysteretic systems.” ASCE Journal of Engineering Mechanics, 102(2): 249–263.
48. Wen, J., Han, Q., Du, X. (2019) “Shaking table tests of bridge model with friction sliding bearings under bi-directional earthquake excitations.” Structure and Infrastructure Engineering, 15(9): 1264–1278.
49. Zhang, H., Liang, X., Gao, Z., Zhu, X. (2020) “Seismic performance analysis of a largescale single-layer lattice dome with a hybrid three-directional seismic isolation system.” Engineering structures, 214: 1–16.
50. 周雲，龔健，鄧雪松 (2012) “變曲率摩擦複擺隔震支承的簡化分析與數值仿真” 工程力學，第二十九卷，第七期，第163–185頁。
51. 吳陽 (2018) “雙擺變曲率滑動隔震支承於雙向震波作用下之實驗與理論研究” 國立成功大學碩士論文，7月，指導教授：盧煉元。
52. 國家地震工程研究中心網頁，雙軸向動態測試系統。檢自http://www.ncree.narl.org.tw/about/laboratory/page/103 (June. 16, 2020)
53. 曾旭玟 (2004) “高分子材料於結構隔震技術之應用” 國立高雄第一科技大學碩士論文，一月，指導教授：盧煉元。
54. 湯宇仕 (2018) “考量近斷層震波作用下之隔震建物機率式耐震評估法” 國立成功大學碩士論文，7月，指導教授：盧煉元。
55. 黃瀚緯 (2019) “雙擺變曲率滑動隔震支承之雙向動力實驗驗證研究” 國立成功大學碩士論文，7月，指導教授：盧煉元。
56. 黃震興、盧煉元、汪向榮、林旺春、楊卓諺、游忠翰、劉瓊琳、林晉丞、賴怡琳、徐安 (2019) “台南實驗室BATS 系統動態性能評估試驗” 2019國家地震工程研究中心實驗成果研討會論文集(II)，報告編號NCREE-19-015，第27–32頁。
57. 盧煉元、林建宏、林錦隆 (2004a) “非線性狀態空間法於消能結構分析之應用”，中國土木水利工程學刊，第十六卷，第四期，第621–634頁。
58. 盧煉元、施明祥、吳政彥 (2004b) “變曲率滑動隔震支承之遲滯行為理論與實驗研究”，第七屆結構工程研討會，桃園大溪，8月22-24日，論文編號：H19。
59. 盧煉元、吳政彥、葉弈麟 (2009) “圓錐形摩擦單擺支承之隔震應用研究”，結構工程，第二十四卷，第二期，第91–116頁。(NSC 94-2625-Z-327-004)