Structural Engineering and Mechanics

  • 제46권1호
  • /
  • Pages.19-37
  • /
  • 2013
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Optimal design of Base Isolation System considering uncertain bounded system parameters

  • Roy, Bijan Kumar (Department of Civil Engineering, Bengal Engineering and Science University) ;
  • Chakraborty, Subrata (Department of Civil Engineering, Bengal Engineering and Science University)
  • 투고 : 2012.06.30
  • 심사 : 2013.02.19
  • 발행 : 2013.04.10
⟨ 이전 논문 다음 논문 ⟩

초록

The optimum design of base isolation system considering model parameter uncertainty is usually performed by using the unconditional response of structure obtained by the total probability theory, as the performance index. Though, the probabilistic approach is powerful, it cannot be applied when the maximum possible ranges of variations are known and can be only modelled as uncertain but bounded type. In such cases, the interval analysis method is a viable alternative. The present study focuses on the bounded optimization of base isolation system to mitigate the seismic vibration effect of structures characterized by bounded type system parameters. With this intention in view, the conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems correspond to a lower bound and upper bound optimum solutions. A lead rubber bearing isolating a multi-storeyed building frame is considered for numerical study to elucidate the proposed bounded optimization procedure and the optimum performance of the isolation system.

키워드

참고문헌

  1. Baratta, A. and Corbi, O. (2002), "On the dynamic behaviour of elastic-plastic structures equipped with pseudoelastic SMA reinforcements", International Journalof Computational Materials Science, 25(1-2), 1-13. https://doi.org/10.1016/S0927-0256(02)00245-8
  2. Baratta, A. and Corbi, O. (2003), "Dynamic response and control of hysteretic structures", International Journal of Simulation Modelling Practice and Theory, 11(5), 371-385. https://doi.org/10.1016/S1569-190X(03)00058-3
  3. Baratta, A. and Corbi, I. (2004), "Optimal design of base-isolators in multi-storey buildings", Computers and Structures, 82(23-26), 2199-2209. https://doi.org/10.1016/j.compstruc.2004.03.061
  4. Bouc, R. (1967), "Forced vibration of mechanical systems with hysteresis", Proceedings of the 4th Conference on Nonlinear Oscillation, Czechoslovakia, Prague, September.
  5. Bucher, C. (2009), "Probability-based optimal design of friction-based seismic isolation devices", Structural Safety, 31(6), 500-507. https://doi.org/10.1016/j.strusafe.2009.06.009
  6. Buckle, I.G. and Mayes, R.L. (1990), "Seismic isolation: history, application, and performance-a world view", Earthquake Spectra, 6(2), 161-201. https://doi.org/10.1193/1.1585564
  7. Chakraborty, S. and Roy, B.K. (2011), "Reliability based optimum design of tuned mass damper in seismic vibration control of structures with bounded uncertain parameters", Probabilistic Engineering Mechanics, 26(2), 215-221. https://doi.org/10.1016/j.probengmech.2010.07.007
  8. Chaudhuri, A. and Chakraborty, S. (2004), "Sensitivity evaluation in seismic reliability analysis of structures", Computer Methods in Applied Mechanics and Engineering, 193(1-2), 59-68. https://doi.org/10.1016/j.cma.2003.09.007
  9. Chaudhuri, A. and Chakraborty, S. (2006), "Reliability of linear structures with parameter uncertainty under non-stationary earthquake", Structural Safety, 28(3), 231-246. https://doi.org/10.1016/j.strusafe.2005.07.001
  10. Chen, S.H. and Zhang, X.M. (2006), "Dynamic response of closed-loop system with uncertain parameters using interval finite-element method", ASCE Journal of Engineering Mechanics, 132(8), 830-840. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:8(830)
  11. Chen, S.H., Song, M. and Chen, Y.D. (2007), "Robustness analysis of responses of vibration control structures with uncertain parameters using interval algorithm", Structural Safety, 29(2), 94-111. https://doi.org/10.1016/j.strusafe.2006.03.001
  12. Constantinou, M.C. and Tadjbakhsh, I.G. (1985), "Hysteretic dampers in base isolation: random approach", ASCE Journal of Structural Engineering, 111(4), 705-721. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(705)
  13. Debbarma, R., Chakraborty, S. and Ghosh, S. (2010), "Unconditional reliability based design of tuned liquid column dampers under stochastic earthquake load considering system parameter uncertainties", Journal of Earthquake Engineering, 14(7), 970-988. https://doi.org/10.1080/13632461003611103
  14. Housner, G.W., Bergman, L.A., Caughey, T.K., Chassiakos, A.G., Claus, R.O., Masri, S.F., Skelton, R.E., Soong, T.T., Spencer, Jr., B.F. and Yao, J.T.P. (1997), "Structural control: past, present and future", ASCE Journal of Engineering Mechanics, 123(9), 897-971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897)
  15. Hurtado, J.E. and Barbat, A.H. (2000), "Equivalent linearization of the Bouc-Wen hysteretic model", Engineering Structures, 22(9), 1121-1132. https://doi.org/10.1016/S0141-0296(99)00056-5
  16. Jangid, R.S. and Datta, T.K. (1995), "Seismic behaviour of base-isolated buildings: a state-of-the-art review", Proceedings of the ICE - Structures and Buildings, 110(2), 186-203. https://doi.org/10.1680/istbu.1995.27599
  17. Jangid, R.S. (2010), "Stochastic response of building frames isolated by lead-rubber bearings", Structural Control and Health Monitoring, 17(1), 1-22. https://doi.org/10.1002/stc.266
  18. Jensen, H.A. (2005), "Design and Sensitivity analysis of dynamical systems subjected to stochastic loading", Computers and Structures, 83(14), 1062-1075. https://doi.org/10.1016/j.compstruc.2004.11.016
  19. Jensen, H.A. and Sepulveda, J.G. (2011), "On the reliability-based design of structures including passive energy dissipation systems", Structural Safety, 34(1), 390-400.
  20. Juhn, G. and Manolis, G.D. (1992), "Stochastic sensitivity and uncertainty of secondary systems in baseisolated structures", Journal of Sound and Vibration, 159(2), 207-222. https://doi.org/10.1016/0022-460X(92)90032-S
  21. Karabork, T. (2011), "Performance of multi-storey structures with high damping rubber bearing Base Isolation systems", Structural Engineering and Mechanics, 39(3), 399-410. https://doi.org/10.12989/sem.2011.39.3.399
  22. Kanai, K. (1957), "Semi-empirical formula for the seismic characteristics of the ground", Bulletin of Earthquake Research Institute, University of Tokyo, 35, 309-325.
  23. Kelly, J.M. (1986), "A seismic base isolation: review and bibliography", Soil Dynamics and Earthquake Engineering, 5(3), 202-216. https://doi.org/10.1016/0267-7261(86)90006-0
  24. Kawano, K., Arakawa, K., Thwe, M. and Venkastaramana, K. (2002), "Seismic response evaluations of base-isolated structures with uncertainties", Proceedings of the Second International Conference on Structural Stability and Dynamics, Singapore, December.
  25. Lin, S., Ahmadi, G. and Tadjbakhsh, I.G. (1990), "Responses of base-isolated shear beam structures to random excitations", Probabilistic Engineering Mechanics, 5(1), 35-46. https://doi.org/10.1016/0266-8920(90)90031-E
  26. Lutes, L.D. and Sarkani, S. (1997), Stochastic analysis of structural and mechanical vibrations, Prentice Hall, NJ.
  27. Matsagar, V.A. and Jangid, R.S. (2004), "Influence of isolator characteristics on the response of baseisolated structures", Engineering Structures, 26(12), 1735-1749. https://doi.org/10.1016/j.engstruct.2004.06.011
  28. McWilliam, S. (2001), "Anti-optimisation of structures using interval analysis", Computers and Structures, 79(4), 421-430. https://doi.org/10.1016/S0045-7949(00)00143-7
  29. Nagai, T. and Nishitani, A. (2005), "Equivalent linearization approachto probabilistic response evaluation for base-isolated buildings," Proceedings of the 9th International Conference on Structural Safety and Reliability ICOSSAR, Eds. G. Augusti, G.I. Schueller, M. Ciampoli, Millpress, Rome, June.
  30. Nigam, N.C. (1972), "Structural optimization in random vibration environment", AIAA Journal, 10(4), 551- 553. https://doi.org/10.2514/3.50151
  31. Papadimitriou, C., Katafygiotis, L.S. and Au, S.K. (1997), "Effects of structural uncertainties on TMD design: A reliability based approach", Journal of Structural Control, 4(1), 65-88. https://doi.org/10.1002/stc.4300040108
  32. Qiu, Z. and Wang, X. (2003), "Comparison of dynamic response of structures with uncertain-but-bounded parameters using non probabilistic interval analysis method and probabilistic approach", Int. Journal of Solids and Structures, 40(20), 5423-5439. https://doi.org/10.1016/S0020-7683(03)00282-8
  33. Roberts, J.B. and Spanos, P.D. (2003), Random Vibration and Statistical Linearization, John Wiley and Sons, New York.
  34. Schueller, G.I. and Jensen, H.A. (2008), "Computational methods in optimization considering uncertaintiesan overview", Computer Method in Applied Mechanics and Engineering, 198(1), 2-13. https://doi.org/10.1016/j.cma.2008.05.004
  35. Scruggs, J.T., Taflanidis, A.A. and Beck, J.L. (2006), "Reliability-based control optimization for active base isolation systems", Structural Control and Health Monitoring, 13(2-3), 705-723. https://doi.org/10.1002/stc.107
  36. Soong, T.T. and Dargush, G.F. (1997), Passive Energy Dissipation Systems in Structural Engineering, John Wiley and Sons, New York.
  37. Spencer, Jr., B.F. and Nagarajaiah, S. (2003), "State of the art of structural control", ASCE Journal of Structural Engineering, 129(7), 845-856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)
  38. Symans, M.D. and Constantinou, M.C. (1999), "Semi-Active Control Systems for Seismic Protection of Structures: A State-of-the-Art Review", Engineering Structures, 21(6), 469-487. https://doi.org/10.1016/S0141-0296(97)00225-3
  39. Taflanidis, A.A., Scruggs, J.T. and Beck, J.L. (2008a), "Reliability-based performance objectives and probabilistic robustness in structural control applications", ASCE Journal of Engineering Mechanics, 134(4), 291-301. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:4(291)
  40. Taflanidis, A.A., Jeffrey, T.S. and Beck, J.L. (2008b), "Probabilistically robust nonlinear design of control systems for base-isolated structures", Structural Control and Health Monitoring, 15(5), 697-719. https://doi.org/10.1002/stc.275
  41. Taflanidis, A.A. and Jia, G. (2011), "A simulation-based framework for risk assessment and probabilistic sensitivity analysis of base-isolated structures", Earthquake Engineering and Structure Dynamics, 40(14), 1629-1651. https://doi.org/10.1002/eqe.1113
  42. Tajimi, H.A. (1960), "Statistical method of determining the maximum response of a building structure during an earthquake", Proceedings of the 2nd World Conference on Earthquake Engineering, Tokyo, July.
  43. Wen, Y.K. (1976), "Method of random vibration of hysteretic systems", ASCE Journal of Engineering Mechanics, 102(2), 249-263.
  44. Zhao, Y.G., Ono, T. and Idota, H. (1999), "Response uncertainty and time-variant reliability analysis for hysteretic MDF structures", Earthquake Engineering and Structure Dynamics, 28(10), 1187-1213. https://doi.org/10.1002/(SICI)1096-9845(199910)28:10<1187::AID-EQE863>3.0.CO;2-E
  45. Zhou, J., Wen, C. and Cai, W. (2006), "Adaptive Control of a base isolated System for protection of building Structures", Journal of Vibration and Acoustics, 128(2), 261-268. https://doi.org/10.1115/1.2159044
  46. Zhou, J. and Wen, C. (2008), "Control of a Hysteretic Structural System in Base Isolation Scheme, Adaptive back stepping Control of Uncertain Systems", Lecture Notes in Control & Information Sciences, 372, 199-213.

피인용 문헌

  1. Reliability-based design of semi-rigidly connected base-isolated buildings subjected to stochastic near-fault excitations vol.11, pp.4, 2016, https://doi.org/10.12989/eas.2016.11.4.701
  2. Incorporation preference for rubber-steel bearing isolation in retrofitting existing multi storied building vol.16, pp.4, 2015, https://doi.org/10.12989/cac.2015.16.4.503
  3. Optimum Performance of Bridge Isolation System under Parameter Uncertainty vol.8, pp.2, 2017, https://doi.org/10.4018/IJGEE.2017070105