The Hysteresis Bouc-Wen Model, a Survey

Archives of Computational Methods in Engineering - Tập 16 - Trang 161-188 - 2009
Mohammed Ismail1, Fayçal Ikhouane2, José Rodellar1
1Dept. of Applied Mathematics III, School of Civil Engineering, Technical University of Catalonia, Barcelona, Spain
2Dept. of Applied Mathematics III, Technical School of Industrial Engineering of Barcelona, Technical University of Catalonia, Barcelona, Spain

Tóm tắt

Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

Tài liệu tham khảo

Abe M, Yoshida J, Fujino Y (2004) Multiaxial behaviors of laminated rubber bearings and their modeling. ii: Modeling. J Struct Eng 130:1133–1144 Acho L, Pozo F (2009) Sliding mode control of hysteretic structural systems. Int J Innov Comput Inf Control 5(4):1–7 Adewuya AA (1996) New methods in genetic search with real-valued chromosomes. Master’s thesis, Massachusetts Institute of Technology, Cambridge Al-Hussaini TM, Zayas VA, Constantinou MC (1994) Seismic isolation of a multi-story frame structure using spherical sliding isolation systems. Technical report, NCEER-94-0007, National Center of Earthquake Engineering Research, Buffalo Aldemir U (2003) Optimal control of structures with semiactive-tuned mass dampers. J Sound Vib 266(4):847–874 Alhan C, Gavin H (2004) A parametric study of linear and non-linear passively damped seismic isolation systems for buildings. Eng Struct 26(4):485–497 Almazan JL, De la Llera JC (2003) Physical model for dynamic analysis of structures with FPS isolators. Earthquake Eng Struct Dyn 32:1157–1184 Alvarez L, Jimenez R (2003) Semi-active control of civil structures using magnetorheological dampers. In: Proceedings of the American control conference, Denver, 4–6 June 2003 An J, Kwon D (2003) Modeling of a magnetorheological actuator including magnetic hysteresis. J Intell Mater Syst Struct 14:541–550 Andrieu-Renaud C, Sudret B, Lemaire M (2004) The phi2 method: a way to compute time-variant reliability. Reliab Eng Syst Saf 84:75–86 Andronikou AM, Bekey GA, Masri SF (1982) Identification of non-linear hysteretic systems using random search. In: IF AC identification and system parameter estimation, Washington, pp 331–336 Andronikou AM, Bekey GA, Hadaegh FY (1983) Identifiability of non-linear systems with hysteretic elements. J Dyn Syst Meas Control 105:209–214 Ang WL, Li WH, Du H (2004) Experimental and modelling approaches of a MR damper performance under harmonic loading. J Inst Eng Singapore 44:1–14 Awrejcewicz J, Dzyubak LP (2005) Evolution of chaotic regions in control parameter planes depending on hysteretic dissipation. Nonlinear Anal 63:155–164 Awrejcewicz J, Dzyubak LP (2005) Influence of hysteretic dissipation on chaotic responses. J Sound Vib 284:513–519 Awrejcewicz J, Dzyubak l (2006) Modeling, chaotic behavior, and control of dissipation properties of hysteretic systems. Math Probl Eng 2006:1–21 Baber TT, Noori YN (1985) Random vibration of degrading pinching systems. J Eng Mech 111:1010–1026 Baber TT, Wen YK (1981) Random vibration of hysteretic degrading systems. J Eng Mech 107(6):1069–1087 Badoni D, Makris N (1996) Nonlinear response of single piles under lateral inertial and seismic loads. Soil Dyn Earthqu Eng 15:29–43 Barbat AH, Rodellar J, Ryan EP, Molinares N (1995) Active control of nonlinear base-isolated buildings. J Eng Mech 121:676–684 Barroso LR, Breneman SE, Smith HA (2002) Performance evaluation of controlled steel frames under multilevel seismic loads. J Struct Eng 128:1368–1378 Barroso LR, Hunt S, Chase JG (2002) Application of magneto-rheological dampers for multi-level seismic hazard mitigation of hysteretic structures. In: 15th ASCE engineering mechanics conference, Columbia University, New York, 2–5 June 2002 Basili M, De Angelis M (2007) Optimal passive control of adjacent structures interconnected with nonlinear hysteretic devices. J Sound Vib 301:106–125 Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, New York Battaini M, Casciati F (1996) Chaotic behavior of hysteretic oscillators. J Struct Control 3(1–2):7–19 Battaini M, Breitung K, Casciati F, Faravelli L (1998) Active control and reliability of a structure under wind excitation. J Wind Eng Ind Aerodyn 74–76:1047–1055 Baz̆ant Z (1978) Endochronic inelasticity and incremental plasticity. Int J Solids Struct 14:691–714 Bazant ZP, Krizek RJ, Shieh CL (1983) Hysteretic endochronic theory for sand. J Eng Mech 109:1073–1095 Beadle ER, Djuric PM (1997) A fast weighted Bayesian bootstrab filter for nonlinear model state estimation. IEEE Trans Aerosp Electron Syst 33:338–343 Bendat JS, Piersol AG (2000) Random data: analysis and measurement, 3rd edn. Wiley, New York Bernardini D, Vestroni F (2003) Non-isothermal oscillations of pseudoelastic devices. Int J Non-Linear Mech 38(9):1297–1313 Black CJ, Makris N, Aiken ID (2004) Component testing, seismic evaluation and characterization of buckling-restrained braces. J Struct Eng 130:880–894 Boardman PR, Wood BJ, Carr AJ (1983) Union house—a cross-braced structure with energy dissipators. Bull N Z Soc Earthq Eng 16(2):83–97 Bobrow JE, Jabbari F, Thai K (2000) A new approach to shock isolation and vibration suppression using a resetable actuator. J Dyn Syst Meas Control 122:570–573 Bonacina G (1994) Seismic base isolation of gas insulated electrical substations: design, experimental and numerical activities, evaluation of the applicability. In: 10th European conference on earthquake engineering, Vienna, Austria Bonelli A, Bursi OS (2004) Generalized-α methods for seismic structural testing. Earthquake Eng Struct Dyn 33:1067–1102 Bouc R (1967) Forced vibrations of a mechanical system with hysteresis. In: Proc 4th conf on nonlinear oscillations, Prague, Czechoslovakia Bouc R (1971) Modèle mathématique d’hystérésis. Acustica 21:16–25. (A mathematical model for hysteresis) Bouc R, Boussaa D (2002) Drifting response of hysteretic oscillators to stochastic excitation. Int J Non-linear Mech 37:1397–1406 Breitung K (1994) Asympotic approximations for probability integrals. Lecture notes in mathematics, vol 1592. Springer, Berlin Breitung K, Faravelli L (1996) Response surface methods and asymptotic approximations. In: Casciati F, Roberts JB (eds) Mathematical models for structural reliability. CRC Press, Boca Raton, pp 227–286, Chap 5 Breitung K, Casciati F, Faravelli L (1998) Reliability based stability analysis for actively controlled structures. Eng Struct 20(3):211–215 Buckle IG, Mayes RL (1990) Seismic isolation history: application and performance—a world review. Earthq Spectra 6:161–201 Butz T, Von Stryk O (1998) Modelling and simulation of electro- and magnetorheological fluid dampers. Z Angew Math Mech 78:1–22 Caddemi S (1998) Parametric nature of the non-linear hardening plastic constitutive equations and their integration. Eur J Mech A Solids 17(3):479–498 Cai GQ, Lin YK (1990) On randomly excited hysteretic structures. J Appl Mech 57:442–448 Carli F (1999) Nonlinear response of hysteretic oscillator under evolutionary excitation. Adv Eng Softw 30(9–11):621–630 Casciati F (1987) Nonlinear stochastic dynamics of large structural systems by equivalent linearization. In: Proc, 5th int conf on application of statistics and probability in soil and structural engineering, ICASP5, Vancouver, Canada Casciati F (1988) Smoothed plasticity laws and elasto-plastic analysis. Technical report, Dipartamento di Ingegneria Strutturale e Geotecnica. Università di Roma “La Sapienza” Casciati F (1989) Stochastic dynamics of hysteretic media. Struct Saf 6:259–269 Chang SI (2004) Bifurcation analysis of a non-linear hysteretic oscillator under harmonic excitation. J Sound Vib 276:215–225 Chang C, Zhou L (2002) Neural network emulation of inverse dynamics for a magnetorheological damper. J Struct Eng 128:231–239 Chase JG, Barroso LR, Hunt S (2003) Quadratic jerk regulation and the seismic control of civil structures. Earthquake Eng Struct Dyn 32:2047–2062 Chase JG, Barroso LR, Hunt S (2004) The impact of total acceleration control for semi-active earthquake hazard mitigation. Eng Struct 26:201–209 Chassiakos AG, Masri SF, Smyth AW, Caughy TK (1998) On-line identification of hysteretic systems. J Appl Mech 65:194–203 Chatzi EN, Triantafillou SP, Koumousis VK (2005) A computer program for 3d inelastic analysis of rc structures. In: 5th GRACM international congress on computational mechanics, Limassol, 29 June–1 July 2005 Chen Y, Ahmadi G (1992) Wind effects on base-isolated structures. J Eng Mech 118:1708–1727 Chen YQ, Soong TT (1988) State-of-the-art review: seismic response of secondary systems. Eng Struct 10:218–228 Chen BM, Lee TH, Hang CC, Guo Y, Weerasooriya S (1999) An H ∞ almost disturbance decoupling robust controller design for a piezoelectric bimorph actuator with hysteresis. IEEE Trans Control Syst Technol 7(2):160–174 Chen Z, Wu ZQ, Yu P (2005) The critical phenomena in a hysteretic model due to the interaction between hysteretic damping and external force. J Sound Vib 284:783–803 Cheng H, Zhu WQ, Ying ZG (2006) Stochastic optimal semi-active control of hysteretic systems by using a magneto-rheological damper. Smart Mater Struct 15(3):711–718 Chiang DY (1999) The generalized masing models for deteriorating hysteresis and cyclic plasticity. Appl Math Model 23:847–863 Chiang DY, Beck JL (1996) A transformation method for implementing classical multi-yield surface theory using the hardening rule of MROZ. Int J Solids Struct 33(28):4239–4261 Ching J, Beck JL, Porter KA (2004) Real-time Bayesian damage detection for uncertain dynamical systems. In: 17th ASCE engineering mechanics conference, University of Delware, Newark, 13–16 June 2004 Ching J, Beck JL, Porter KA (2006) Bayesian state and parameter estimation of uncertain dynamical systems. Probab Eng Mech 21:81–96 Cho S, Kim B, Jung H, Lee I (2005) Implementation of modal control for seismically excited structures using magnetorheological dampers. J Eng Mech 131:177–184 Choi Y, Wereley NM (2002) Comparative analysis of the time response of electrorheological and magnetorheological dampers using nondimensional parameters. J Intel Mater Syst Struct 13:443–451 Choi SB, Lee SK, Park YP (2001) A hysteresis model for the field-dependent damping force of a magnetorheological damper. J Sound Vib 245:375–383 Choi K, Cho S, Jung H, Lee I (2004) Semi-active fuzzy control for seismic response reduction using magnetorheological dampers. Earthquake Eng Struct Dyn 33:723–736 Christenson RE, Spencer BF, Johnson EA (2002) Experimental studies on the smart damping of stay cables. In: ASCE structures congress, Denver, Colorado, 4–6 April 2002 Ciampi V, De Angelis M (1996) Optimal design of passive control systems based on energy dissipation for earthquake protection of structures. In: Proceedings of the third European conference on structural dynamics, EURODYN ’96, Firenze, Italia, pp 525–532 Clarke RP (2005) Non-Bouc degrading hysteresis model for nonlinear dynamic procedure seismic design. J Struct Eng 131:287–291 Colangelo F, Giannini R, Pinto PE (1996) Seismic reliability analysis of reinforced concrete structures with stochastic properties. Struct Saf 18(2–3):151–168 Constantinou MC, Andane MA (1987) Dynamics of soil-base-isolated structure systems: evaluation of two models for yielding systems. Technical report, Department of Civil Engineering, Drexel University, Philadelphia Constantinou MC, Tadjbakhsh IG (1985) Hysteretic dampers in base isolation: Random approach. J Struct Eng 111:705–721 Constantinou M, Mokha A, Reinhorn A (1990) Teflon bearings in base isolation. ii: Modeling. J Struct Eng 116(2):455–474 Corbi O (2003) Shape memory alloys and their application in structural oscillations attenuation. Simul Model Pract Theory 11(5–6):387–402 Dai Z, Huang J, Wang H (2004) Semi-active control of a cable-stayed bridge under multiple-support excitations. J Zhejiang Univ Sci 5(3):317–325 Dang X, Tan Y (2005) An inner product-based dynamic neural network hysteresis model for piezoceramic actuators. Sens Actuators A Phys 121:535–542 De la Llera JC, Esguerra C, Almazán JL (2004) Earthquake behavior of structures with copper energy dissipators. Earthquake Eng Struct Dyn 33:329–358 Deacon B, Worden K (1996) Identification of hysteretic systems using genetic algorithms. In: EU ROMECH–second European nonlinear oscillation conference, Prague Deb SK (2004) Seismic base isolation—an overview. Current Sci Special Sect Geotech Earthq Hazards 87:1426–1430 Demetriades GF, Constantinou MC, Reinhorn AM (1993) Study of wire rope systems for seismic protection of equipment in buildings. Eng Struct 15(5):321–334 Derham CJ, Kelly JM, Tomas AG (1985) Nonlinear natural rubber bearings for seismic isolation. Nucl Eng Des 84(3):417–428 Dimizas PC, Koumousis VK (2005) System identification of non-linear hysteretic systems with application to friction pendulum isolation systems. In: 5th GRACM international congress on computational mechanics, Limassol, 29 June–1 July 2005 Dimizas P, Koumousis V (2006) Decay law for the hysteretic Bouc-wen model. In: 2nd international conference on nonlinear normal modes and localization in vibrating systems, Samos, 19–23 June 2006 Dobson S, Noori M, Hou Z, Dimentberg M, Barber T (1997) Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis. Int J Non-linear Mech 32(4):669–680 Dominguez A, Sedaghati R, Stiharu I (2004) Modeling the hysteresis phenomenon of magnetorheological dampers. Smart Mater Struct 13:1351–1361 Dominguez A, Sedaghati R, Stiharu I (2006) A new dynamic hysteresis model for the magnetorheological dampers. Smart Mater Struct 15(5):1179–1189 Dominguez A, Sedaghati R, Stiharu I (2008) Modeling and application of mr dampers in semi-adaptive structures. Comput Struct 86:407–415 Dong S, Lu KQ, Sun JQ, Rudolph K (2005) Rehabilitation device with variable resistance and intelligent control. Med Eng Phys 27(3):249–255 Draper NR, Smith H (1981) Applied regression analysis. Wiley, New York Du H, Sze KY, Lam J (2005) Semi-active h infinity control of vehicle suspension with magneto-rheological dampers. J Sound Vib 283(3–5):981–996 Dyke SJ (2005) Current directions in structural control in the us. In: 9th world seminar on seismic isolation, energy dissipation and active vibration control of structures, Kobe, Japan, 13–16 June 2005 Dyke SJ, Spencer BF, Sain MK, Carlson JD (1996) Experimental verification of semiactive structural control strategies using acceleration feedback. In: Proc 3rd int conf on motion and vibration control, vol 3, Japan Society of Mechanical Engineers, Tokyo, pp 291–296 Dyke SJ, Spencer BF, Sain MK, Carlson JD (1996) Modeling and control of magnetorheological dampers for seismic response reduction. Smart Mater Struct 5:565–575 Ellingwood BR (2001) Earthquake risk assessment of building structures. Reliab Eng Syst Saf 74:251–262 Erkus B, Abé M, Fujino Y (2002) Investigation of semi-active control for seismic protection of elevated highway bridges. Eng Struct 24:281–293 Erlicher S, Point N (2004) Thermodynamic admissibility of Bouc-Wen type hysteresis models. C R Méc 332(1):51–57 Fenz DM, Constantinou MC (2008) Spherical sliding isolation bearings with adaptive behavior: Theory. Earthquake Eng Struct Dyn 37:163–183 Fenz DM, Constantinou MC (2008) Spherical sliding isolation bearings with adaptive behavior: Experimental verification. Earthquake Eng Struct Dyn 37:185–205 Filiatrault A, Lee G, Aref A, Bruneau M, Constantinou M, Reinhorn A, Whittaker A (2004) Recent progress towards the seismic control of structural and non-structural systems in hospitals. Technical report, 36th technical meeting on panel on wind and seismic effects, Gaithersburg, MD, Multidisciplinary Centre for Earthquake Engineering Research (MCEER), State University of New York at Buffalo, Buffalo, 17–22 May 2004 Fletcher R (1980) Practical methods of optimization. Wiley, New York Foliente GC (1995) Hysteresis modeling of wood joints and structural systems. J Struct Eng 121(6):1013–1022 Foliente GC, Signh MP, Noori MN (1996) Equivalent linearization of generally pinching hysteretic, degrading systems. Earthquake Eng Struct Dyn 25:611–629 Gavin HP (2001) Control of seismically excited vibration using electrorheological materials and Lyapunov methods. IEEE Trans Control Syst Technol 9(1):27–36 Gavin HP (2001) Multi-duct ER dampers. J Intell Mater Syst Struct 12:353–366 Gavin HP, Zaicenco A (2007) Performance and reliability of semi-active equipment isolation. J Sound Vib 306:74–90 Gerolymos N, Gazetas G (2006) Static and dynamic response of massive caisson foundations with soil and interfacenonlinearities-validation and results. Soil Dyn Earthq Eng 26:377–394 Gerolymos N, Gazetas G (2006) Winkler model for lateral response of rigid caisson foundations in linear soil. Soil Dyn Earthq Eng 26(5):347–361 Gerolymos N, Gazetas G (2007) A model for grain-crushing-induced landslides-application to nikawa, Kobe 1995. Soil Dyn Earthq Eng 27:803–817 Giuclea M, Sireteanu T, Stancioiu D, Stammers CW (2004) Modelling of magnetorheological damper dynamic behaviour by genetic algorithms based inverse method. Proc Rom Acad Ser A 5(1) Guggenberger J, Grundmann H (2004) Monte Carlo simulation of the hysteretic response of frame structures using plastification adapted shape functions. Probab Eng Mech 19:81–91 Guggenberger J, Grundmann H (2005) Stochastic response of large FEM models with hysteretic behavior in beam elements. Comput Methods Appl Mech Eng 194(12–16):1739–1756 Gunstona TP, Rebelleb J, Griffina MJ (2004) A comparison of two methods of simulating seat suspension dynamic performance. J Sound Vib 278:117–134 Guo AX, Xu YL, Wu B (2002) Seismic reliability analysis of hysteretic structure with viscoelastic dampers. Eng Struct 24(3):373–383 Guo S, Yang S, Pan C (2006) Dynamic modeling of magnetorheological damper behaviors. J Intell Mat Syst Struct 17:3–14 Ha JL, Fung RF, Han C (2005) Optimization of an impact drive mechanism based on real-coded genetic algorithm. Sens Actuators A Phys 121(2):488–493 Ha JL, Fung RF, Yang CS (2005) Hysteresis identification and dynamic responses of the impact drive mechanism. J Sound Vib 283:943–956 Ha J, Kung Y, Fungc R, Hsien S (2006) A comparison of fitness functions for the identification of a piezoelectric hysteretic actuator based on the real-coded genetic algorithm. Sens Actuators A 132:643–650 Hamidi M, El Naggar MH (2007) On the performance of SCF in seismic isolation of the interior equipment of buildings. Earthquake Eng Struct Dyn 36:1581–1604 Hamidi M, El Naggar MH, Vafai A, Ahmadi G (2003) Seismic isolation of buildings with sliding concave foundation (SCF). Earthquake Eng Struct Dyn 32:15–29 Han YM, Lim SC, Lee HG, Choi SB, Choi HJ (2003) Hysteresis identification of polymethylaniline-based ER fluid using Preisach model. Mater Des 24:53–61 Haukaasa T, Kiureghian AD (2006) Strategies for finding the design point in non-linear finite element reliability analysis. Probab Eng Mech 21(21):133–147 Haupt RL, Haupt SE (1998) Practical genetic algorithms. Wiley, New York He WL, Agrawal AK (2002) Energy transfer approach for the design of passive energy dissipation systems. In: 15th ASCE engineering mechanics conference, Columbia University, New York, 2–5 June 2002 Hong SR, Choi SB, Choi YT, Wereley NM (2005) A hydro-mechanical model for hysteretic damping force prediction of ER damper: experimental verification. J Sound Vib 285:1180–1188 Hornig KH (2000) Parameter characterization of the Bouc-wen mechanical hysteresis model for sandwich composite materials by using real coded genetic algorithms. Technical report, Auburn University, Mechanical Engineering Department, 201 Ross Hall, Auburn, AL 36849 Horr AM, Safi M, Asadpour N (2002) Seismic analysis of Tehran telecommunication tower using complex fractional modulus. Struct Des Tall Build 11:353–373 Hoshiya M, Maruyama O (1988) Kalman filtering of versatile restoring systems. Technical report, Department of Civil Engineering, Musashi Institute of Technology, 1-28-1, Tamazutmsumi Setagaya-ku, Tokyo 158, Japan Hurtado JE, Barbat AH (1996) Improved stochastic linearization method using mixed distributions. Struct Saf 18(1):49–62 Hurtado JE, Barbat AH (1998) Fourier-based maximum entropy method in stochastic dynamics. Struct Saf 20:221–235 Hurtado JE, Barbat AH (2000) Equivalent linearization of the Bouc-wen hysteretic model. Eng Struct 22:1121–1132 Igusa T, Der Kiureghian A (1985) Dynamic characterisation of two-degree-of-freedom equipment-structure system. J Eng Mech 111:1–19 Ikhouane F, Dyke SJ (2007) Modeling and identification of a shear mode magnetorheological damper. Smart Mater Struct 16(3):605–616 Ikhouane F, Gomis-Bellmunt O (2008) A limit cycle approach for the parametric identification of hysteretic systems. Syst Control Lett 57:663–669 Ikhouane F, Rodellar J (2005) On the hysteretic Bouc-Wen model. Part I: Forced limit cycle characterization. Nonlinear Dyn 42:63–78 Ikhouane F, Rodellar J (2005) On the hysteretic Bouc-Wen model. Part II: Robust parametric identification. Nonlinear Dyn 42:79–95 Ikhouane F, Rodellar J (2006) A linear controller for hysteretic systems. IEEE Trans Automat Control 51(2):340–344 Ikhouane F, Rodellar J (2007) Systems with hysteresis: analysis, identification and control using the Bouc-Wen model. Wiley, New York Ikhouane F, Mañosa V, Rodellar J (2004) Bounded and dissipative solutions of the Bouc-Wen model for hysteretic structural systems. In: Proceedings of the American control conference, Boston, pp 3520–3524 Ikhouane F, Mañosa V, Rodellar J (2005) Adaptive control of a hysteretic structural system. Automatica 41:225–231 Ikhouane F, Hurtado JE, Rodellar J (2007) Variation of the hysteresis loop with the Bouc-Wen model parameters. Nonlinear Dyn 48(4):361–380 Ikhouane F, Mañosa V, Rodellar J (2007) Dynamic properties of the hysteretic Bouc-Wen model. Syst Control Lett 56:197–205 Inaudi JA (1997) Modulated homogeneous friction: a semi-active damping strategy. Earthquake Eng Struct Dyn 26(3):361–376 Inaudi J, Lopez Almansa F, Kelly JM, Rodellar J (1992) Predictive control of base isolated structures. Earthquake Eng Struct Dyn 21:471–482 Ioannou PA, Sun J (1996) Robust adaptive control. Prentice Hall, New York Irschik H, Schacher K, Kugi A (1998) Control of earthquake excited nonlinear structures using Lyapunov’s theory. Comput Struct 67:83–90 Ismail M, Rodellar J, Ikhouane F (2008) A new isolation device for equipment protection. In: 4th European conference on structural control, Saint Petersburg, Russia, 8–12 September 2008, pp 359–366 Ismail M, Rodellar J, Ikhouane F (2008) A new approach to rolling-based seismic isolators for light- to moderate structures. In: The 14th world conference on earthquake engineering, Beijing, China, number S25-012, 12–17 October 2008 Jangid RS, Datta TK (1995) Seismic behavior of base isolated building: A state-of-the-art-review. Struct Build 110(2):186–203 Jangid RS, Kelly JM (2000) Torsional displacements in base-isolated buildings. Earthq Spectra 16:443–454 Jansen LM, Dyke SJ (2000) Semi-active control strategies for MR dampers: A comparative study. J Eng Mech 126(8):795–803 Ji H, Moon Y, Kim C, Lee I (2005) Structural vibration control using semiactive tuned mass damper. In: The eighteenth KKCNN symposium on civil engineering-KAIST6, Taiwan, 18–20 December 2005 Jiménez R, Alvarez-Icaza L (2004) Civil structures semi-active control with limited measurements. In: Proceeding of the 2004 American control conference, Boston, 30 June–2 July 2004 Juhn G, Manolis GD, Constantinou M (1992) Experimental study of secondary systems in a base isolated structure. J Struct Eng 118(8):2204–2221 Jung BH, Ruangrassamee A, Kawashima K, Spencer BF, Lee I (2002) Seismic protection of nonlinear coupled bridge systems using semi-active control strategy. KSCE J Civil Eng Struct Eng 6(1):47–60 Jung H, Spencer BF, Lee I (2003) Control of seismically excited cable-stayed bridge employing magnetorheological fluid dampers. J Struct Eng 129:873–883 Kafal C, Grigoriu M (2004) Seismic fragility analysis. In: 9th ASCE specialty conference on probabilistic mechanics and structural reliability Karray MA, Bouc R (1989) Etude dynamique d’un système d’isolation antisismique. Ann ENIT 3(1):43–60 Katsikadelis JT, Kallivokas LF (1988) Plates on biparametric elastic foundation by BDIE method. J Eng Mech 114:847–832 Kelly JM (1982) The influence of base isolation on the seismic response of light secondary equipment. Technical report, UCB/EERC-81/17, Earthquake engineering research center, University of California, Berkeley Kelly JM (1986) Seismic base isolation: Review and bibliography. Soil Dyn Earthq Eng 5:202–216 Kelly JM (1991) Base isolation: Origin and development. News Univ Calif Earthq Eng Res Cent 12(1):1–3 Kelly JM (1998) Seismic isolation of civil buildings in the USA. Prog Struct Eng Mater 3:279–285 Kelly TE (2001) Base isolation of structures, design guidlines. Technical report, Holmes Consulting Group Ltd Kelly JM, Tsztoo DF (1977) Earthquake simulation testing of a atepping-frame with energy-absorbing devices. Technical report, Report No UCB/EERC-77/17, Earthquake engineering research center, University of California, Berkely Kerschen G, Worden K, Vakakis AF, Golinval JC (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process 20(3):505–592 Khaloo AR, Tariverdilo S (2002) Localization analysis of reinforced concrete members with softening behavior. J Struct Eng 128:1148–1157 Kim SB, Spencer BF, Yun CB (2005) Frequency domain identification of multi-input, multi-output systems considering physical relationships between measured variables. J Eng Mech 131(5):461–472 Koliopulos PK, Chandler AM (1995) Stochastic linearization of inelastic seismic torsional response: formulation and case studies. Eng Struct 17(7):494–504 Kosmatopoulos EB, Smyth AW, Masri SF, Chassiakos AG (2001) Robust adaptive neural estimation of restoring forces in nonlinear structures. J Appl Mech Trans ASME 68:880–893 Kunnath SK, Mander JB, Fang L (1997) Parameter identification for degrading and pinched hysteretic structural concrete systems. Eng Struct 19(3):224–232 Kwok NM, Ha QP, Nguyen TH, Li J, Samali B (2006) A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization. Sens Actuators A 132:441–451 Kwok NM, Ha QP, Nguyen MT, Li J, Samali B (2007) Bouc-wen model parameter identification for a MR fluid damper using computationally efficient GA. ISA Trans 46:167–179 Kyprianou A, Worden K, Panet M (2001) Identification of hysteresis systems using the differential evolution algorithm. J Sound Vib 2(248):289–314 Lacarbonara W, Bernardini D, Vestroni F (2004) Nonlinear thermomechanical oscillations of shape-memory devices. Int J Solids Struct 41(5–6):1209–1234 Lambrou V, Constantinou MC (1994) Study of seismic isolation systems for computer floors. Technical report, NCEER-94-0020, July 1994 Landau ID, Lozano R, M’Saad M (1997) Adaptive control. Springer, Berlin Laxalde D, Thouverez F, Sinou J (2006) Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber. Int J Non-Linear Mech 41:969–978 Lee T, Kawashima K (2006) Effectiveness of semi-active control on a seismic-excited isolated bridge. In: First European conference on earthquake engineering and seismology, Geneva, Switzerland, 3–8 September 2006 Leger P, Dussault S (1992) Seismic-energy dissipation in MDOF structures. J Struct Eng 118(5):1251–1269 Leitmann G (1994) Semiactive control for vibration attenuation. J Intell Mater Syst Struct 5:841–846 Leva A, Piroddi L (2002) NARX-based technique for the modeling of magneto-rheological damping devices. Smart Mater Struct 11:79–88 Li SJ, Suzuki Y, Noori M (2004) Improvement of parameter estimation for non-linear hysteretic systems with slip by a fast Bayesian bootstrap filter. Int J Non-linear Mech 39:1435–1445 Li SJ, Suzuki Y, Noori M (2004) Identification of hysteretic systems with slip using bootstrap filter. Mech Syst Signal Process 18:781–795 Li SJ, Yu H, Suzuki Y (2004) Identification of non-linear hysteretic systems with slip. Comput Struct 82:157–165 Liao WH, Lai CY (2002) Harmonic analysis of a magnetorheological damper for vibration control. Smart Mater Struct 11:288–296 Liao WH, Wang DH (2003) Semiactive vibration control of train suspension systems via magnetorheological dampers. J Intell Mater Syst Struct 14:161–172 Liao K, Wen Y, Foutch DA (2007) Evaluation of 3D steel moment frames under earthquake excitations. i: Modeling. J Struct Eng 133(3):462–470 Lin J (1994) Extraction of dynamic soil properties using extended Kalman filter. J Geotech Eng 120(12):2100–2117 Lin J, Betti R (2004) On-line identification and damage detection in non-linear structural systems using a variable forgetting factor approach. Earthquake Eng Struct Dyn 33:419–444 Lin TW, Hone CC (1993) Base isoaltion by free rolling rods under basement. Earthquake Eng Struct Dyn 22(3):261–273 Lin C, Yang S (2006) Precise positioning of piezo-actuated stages using hysteresis-observer based control. Mechatronics 16:417–426 Lin JS, Zhang Y (1994) Nonlinear structural identification using extended Kalman filter. Comput Struct 52(4):757–764 Lin J, Betti R, Smyth AW, Longman RW (2001) On-line identification of non-linear hysteretic structural systems using a variable trace approach. Earthquake Eng Struct Dyn 30:1279–1303 Lind NC (1987) Reliability and risk analysis in civil engineering. In: Proceeding of ICASP5, the fifth international conference on applications of statistics and probability in soil and structural engineering, University of British Columbia, Vancouver, Canada Liu H, Teng J (2004) Modeling of smart dampers for vibration control. In: Proceedings of the 2004 international conference on intelligent mechatronics and automation, Chengdu, China, August 2004 Lo HR, Hammond JK, Sainsbury MG (1988) Non-linear system identification and modelling with application to an isolator with hysteresis. In: Proceedings of the 6th international modal analysis conference, vol II, pp 1453–1459 Loh CH, Chung ST (1993) A three-stage identification approach for hysteretic systems. Earthquake Eng Struct Dyn 22:129–150 Loh CH, Cheng CR, Wen YK (1995) Probabilistic evaluation of liquefaction potential under earthquake loading. Soil Dyn Earthqu Eng 14:269–278 Loh C, Wu LY, Lin PY (2003) Displacement control of isolated structures with semi-active control devices. J Struct Control 10:77–100 Low TS, Guo W (1995) Modeling of a three-layer piezoelectric bimorph beam with hysteresis. J Microelectromechanical Syst 4(4):230–237 Lu X, Zhou Q (2002) Dynamic analysis method of a combined energy dissipation system and its experimental verification. Earthquake Eng Struct Dyn 31:1251–1265 Luo N, Rodellar J, de la Sen M (1998) Composite robust active control of seismically excited structures with actuator dynamics. Earthquake Eng Struct Dyn 27:301–311 Luo N, Rodellar J, de la Sen M, Vehi J (2000) Output feedback sliding mode control of base isolated structures. J Franklin Inst 337(5):555–577 Luo N, Rodellar J, Vehi J, de la Sen M (2001) Composite semiactive control of seismically excited structures. J Franklin Inst 338(2–3):225–240 Ma F, Zhang H, Bockstedte A, Foliente GC, Paevere P (2004) Parameter analysis of the differential model of hysteresis. J Appl Mech 71:342–349 Ma F, Ng CH, Ajavakom N (2006) On system identification and response prediction of degrading structures. Struct Control Health Monit 13:347–364 Mack JW, Nistri P, Zecca P (1993) Mathematical models for hysteresis. SIAM Rev 35(1):94–123 Makris N, Black CJ (2004) Dimensional analysis of bilinear oscillators under pulse-type excitations. J Eng Mech 130:1019–1031 Makris N, Deoskar HS (1996) Prediction of observed response of base-isolated structure. J Struct Eng 122(5):485–493 Mañosa V, Ikhouane F, Rodellar J (2005) Control of uncertain non-linear systems via adaptive backstepping. J Sound Vib 280:657–680 Marano GC, Greco R (2003) Efficiency of base isolation systems in structural seismic protection and energetic assessment. Earthquake Eng Struct Dyn 32:1505–1531 Marano GC, Greco R (2004) A performance-reliability-based criterion for the optimum design of bridge isolators. ISET J Earthq Technol 41:261–276 Marano GC, Sgobba S (2007) Stochastic energy analysis of seismic isolated bridges. Soil Dyn Earthqu Eng 27:759–773 Maruyama O, Yun CB, Hoshiya M, Shinozuka M (1989) Program exkal2 for identification of structural dynamic systems. Technical report, NCEER-89-0014, National center for earthquake engineering research, Buffalo Masri SF (1994) A hybrid parametric/nonparametric approach for the identification of nonlinear systems. Probab Eng Mech 9:47–57 Masri SF, Smyth A, Chassiakos AG (1995) Adaptive identification for the control of systems incorporating hysteretic elements. In: Proceedings of the international symposium on microsystems, intelligent materials and robots, Japan, pp 419–422 Masri SF, Caffrey JP, Caughey TK, Smyth AW, Chassiakos AG (2004) Identification of the state equation in complex non-linear systems. Int J Non-Linear Mech 39:1111–1127 McClamroch NH, Gavin HP (1995) Closed loop structural control using electrorheological dampers. In: Proc Am control conf American automatic control council, Washington, pp 4173–4177 Mehendale CS, Grigoriadis KM (2004) Hysteresis compensation using lpv gain-scheduling. In: Proceeding of the 2004 American control conference, Boston, 30 June–2 July 2004 Mokha A, Constantinou M, Reinhorn A (1990) Teflon bearings in base isolation. Part I: Testing. J Struct Eng 116(2):438–454 Moon SJ, Bergman LA, Voulgaris PG (2003) Sliding mode control of cable-stayed bridge subjected to seismic excitation. J Eng Mech 129:71–78 Moreschi LM, Singh MP (2003) Design of yielding metallic and friction dampers for optimal seismic performance. Earthquake Eng Struct Dyn 32:1291–1311 Mostaghel N (1984) Resilient-friction base isolator. Technical report, Report No UTEC 84-097, Department of Civil Engineering, University of Utah, Salt Lake City Mostaghel N, Byrd RA (2002) Inversion of Ramberg-Osgood equation and description of hysteresis loops. Int J Non-linear Mech 37:1319–1335 Mostaghel N, Flint BF (1986) Preliminary experimental evaluation of r-fbi bearings. Technical report, Report No UTEC 86-089, Department of Civil Engineering, University of Utah, Salt Lake City Mostaghel N, Kelly JM (1987) Design procedures for the r-fbi bearings. Technical report, Report No UCB/EERC-87/18, Earthquake Engineering Research Center, University of California, Berkely Murnal P, Sinha R (2004) Aseismic design of structure-equipment systems using variable frequency pendulum isolator. Nucl Eng Des 231:129–139 Myslimaj B, Gamble S, Chin-Quee D, Davies A (2003) Base isolation technologies for seismic protection of museum artifacts. In: The 2003 IAMFA annual conference in San Francisco, California, 21–24 September 2003 Naeim F, Kelly JM (1999) Design of seismic isolated structures—from theory to practice. Wiley, New York Narasimhan S, Nagarajaiah S, Johnson EA, Gavin HP (2005) Smart base isolated benchmark building, Part I: Problem definition. J Struct Control 13(2–3):573–588 Nguyen TH, Kwok NM, Ha QP, Li J, Samali B (2006) Adaptive sliding mode control for civil structures using magnetorheological dampers. In: ISARC2006 Ni YQ, Ko JM, Wong CW (1998) Identification of non-linear hysteretic isolators from periodic vibration tests. J Sound Vib 4(217):737–756 Ni YQ, Ko JM, Wong CW (1999) Nonparametric identification of nonlinear hysteretic systems. J Eng Mech 125:206–215 Ni YQ, Ying ZG, Ko JM, Zhu WQ (2002) Random response of integrable Duhem hysteretic systems under non-white excitation. Int J Non-linear Mech 37(8):1407–1419 Noori M, Dimentberg M, Hou Z, Christodoulidou R, Alezandrou A (1995) First-passage study and stationary response analysis of a BWB hysteresis model using quasi-conservative stochastic averaging method. Probab Eng Mech 10:161–170 Ohtori Y, Spencer BF (2002) Semi-implicit integration algorithm for stochastic analysis of multi-degree-of-freedom structures. J Eng Mech 128:635–643 Oka S, Kimb D, Parkc K, Kohb H (2007) Semi-active fuzzy control of cable-stayed bridges using magneto-rheological dampers. Eng Struct 29:776–788 Okuizumi N, Kimura K (2004) Multiple time scale analysis of hysteretic systems subjected to harmonic excitation. J Sound Vib 272:675–701 Ólafsson S, Remseth S, Sigbjörnsson R (2001) Stochastic models for simulation of strong ground motion in Iceland. Earthquake Eng Struct Dyn 30:1305–1331 Oldfield M, Ouyang H, Mottershead JE (2005) Simplified models of bolted joints under harmonic loading. Comput Struct 84:25–33 Onat ET, Drucker DC (1952) Inelastic instability and incremental theories of plasticity. J Aeronaut Sci 20(3):181–186 Panet M, Jezequel L (2000) Dissipative unimodal structural damping identification. Int J Non-linear Mech 35:795–815 Park YJ, Wen YK, Ang AHS (1986) Random vibration of hysteretic systems under bi-directional ground motions. Earthquake Eng Struct Dyn 14(4):543–557 Park KS, Jung HJ, Lee IW (2002) Hybrid control strategies for seismic protection of benchmark cable-stayed bridges. In: Proceedings of the 7th US national conference on earthquake engineering, Boston Park KS, Jung HJ, Lee IW (2003) Hybrid control strategy for seismic protection of a benchmark cable-stayed bridge. Eng Struct 25:405–417 Park K, Jung H, Spencer BF, Lee I (2003) Hybrid control systems for seismic protection of a phase II benchmark cable-stayed bridge. J Struct Control 10:231–247 Pastor N, Ferran AR (2005) Hysteretic modeling of X-braced shear walls. Thin-Walled Struct 43:1567–1588 Pei JS, Smyth AW, Kosmatopoulos EB (2004) Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems. J Sound Vib 275:693–718 Peng B, Conte JP (1997) Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model. Earthquake Eng Struct Dyn 26:895–916 Petrone F, Lacagnina M, Scionti M (2004) Dynamic characterization of elastomers and identification with rheological models. J Sound Vib 271:339–363 Pires JA (1996) Stochastic seismic response analysis of soft soil sites. Nucl Eng Des 160:363–377 Pivovarov I, Vinogradov OG (1987) One application of Bouc’s model for non-linear hysteresis. J Sound Vib 118(2):209–216 Pozo F, Ikhouane F, Rodellar J (2005) Control of hysteretic base-isolated structures: an adaptive backstepping. In: Proceedings of the 44th IEEE conference on decision and control, and the European control conference 2005 Seville, Spain, 12–15 December 2005 Pozo F, Ikhouane F, Pujol G, Rodellar J (2006) Adaptive backstepping control of hysteretic base-isolated structures. J Vib Control 12(4):373–394 Pozo F, Montserrat PM, Rodellar J, Acho L (2008) Robust active control of hysteretic base-isolated structures: application to the benchmark smart base-isolated building. Struct Control Health Monit 15(5):720–736 Pozo F, Acho L, Rodríguez A, Pujol G (2009) Nonlinear modeling of hysteretic systems with double hysteretic loops using position and acceleration information. Nonlinear Dyn. doi:10.1007/s11071-008-9414-7 (to appear) Ramachandran J (2005) Analysis of pile foundations under seismic loading. Technical report, CBE Institute Ramallo JC, Johnson EA, Spencer BF (2002) Smart base isolation systems. J Eng Mech 128:1088–1100 Ramallo JC, Yoshioka H, Spencer BF (2004) A two-step identification technique for semiactive control systems. Struct Control Health Monitoring 11:273–289 Rao SS (1996) Engineering optimization: theory and practice. Wiley, New York Ribakov Y, Gluck J (2002) Selective controlled base isolation system with magnetorheological dampers. Earthquake Eng Struct Dyn 31:1301–1324 Robinson WH, Tucker AG (1977) A lead-rubber shear damper. Bull N Z Soc Earthq Eng 10(3):151–153 Robinson WH, Tucker AG (1983) Test results for lead-rubber bearings for the William M Clayton building, toe bridge, and waiotukupuna bridge. Bull N Z Soc Eng 14(1):21–33 Rodríguez A, Ikhouane F, Rodellar J, Iwata N (2009) Model identification of a large-scale magnetorheological fluid damper. Smart Mater Struct 18(1) Rodríguez A, Ikhouane F, Rodellar J, Luo N (2009) Modeling and identification of a small scale magnetorheological damper. J Intell Mater Syst Struct (to appear) Ryu M, Hong S (1998) End-to-end design of distributed real-time systems. Control Eng Pract 6:93–102 Saad P, Al Majid A, Thouverez F, Dufour R (2006) Equivalent rheological and restoring force models for predicting the harmonic response of elastomer specimens. J Sound Vib 290:619–639 Sain PM, Sain MK, Spencer BF (1997) Models for hysteresis and application to structural control. In: American control conference, June 1997, pp 16–20 Sasani M, Popov EP (2001) Seismic energy dissipators for RC panels: analytical studies. J Eng Mech 127(8):835–843 Savaresi SM, Bittanti S, Montiglio M (2005) Identification of semi-physical and black-box non-linear models: the case of MR-dampers for vehicles control. Automatica 41:113–127 Schenk CA, Pradlwarter HJ, Schuëller GI (2005) Non-stationary response of large, non-linear finite element systems under stochastic loading. Comput Struct 83(14):1086–1102 Shampine LF (1994) Numerical solutions for ordinary differential equations. Chapman & Hall, London Shen Y, Golnaraghi MF, Heppler GR (2005) Analytical and experimental study of the response of a suspension system with a magnetorheological damper. J Intel Mater Syst Struct 16:135–147 Shih MH, Sung WP (2005) A model for hysteretic behavior of rhombic low yield strength added damping and stiffness. Comput Struct 83:895–908 Shih M, Sung W, Go C (2004) Investigation of newly developed added damping and stiffness device with low yield strength steel. J Zhejiang Univ Sci 5(3):326–334 Simeonov VK, Sivaselvan MV, Reinhorn AM (2000) Nonlinear analysis of structural frame system by the state-space approach. Comput-Aided Civil Infrastruct Eng 15:76–89 Sims ND, Stanway R, Johnson AR (1999) Vibration control using smart fluids: A state-of-the-art review. Shock Vib Dig 31(3):195–203 Sims ND, Peel DJ, Stanway R, Johnson AR, Bullough WA (2000) The electrorheological long-stroke damper: A new modelling technique with experimental validation. J Sound Vib 229(2):207–227 Simulescu I, Mochio T, Shinozuka M (1989) Equivalent linearization method in nonlinear FEM. J Eng Mech 115:475–492 Singh MP (1988) Seismic design of secondary systems. Probab Eng Mech 3(3):151–158 Sivaselvan MV, Reinhorn AM (2000) Hysteretic models for deteriorating inelastic structures. J Eng Mech 126:633–640 Sivaselvan MV, Reinhorn AM (2002) Collapse analysis: Large inelastic deformations analysis of planar frames. J Struct Eng 128:1575–1583 Sjöberg M (2002) On dynamic properties of rubber isolators. Technical report, The Marcus Wallenberg laboratory for sound and vibration research, Stockholm Skelton RE (1988) Dynamic systems control: linear systems analysis and synthesis. Wiley, New York Skinner RI, Robinson WH, McVerry GH (1993) An introduction to seismic isolation. Wiley, New York Smith AW, Masri SF, Chassiakos AG, Caughey T.K. (1999) On-line parametric identification of MDOF nonlinear hysteretic systems. J Eng Mech 125(2):133–142 Smith AW, Masri SF, Kosmatopoulos EB, Chassiakos AG, Caughey TK (2002) Development of adaptive modeling techniques for non-linear hysteretic systems. Int J Non-linear Mech 37:1435–1451 Song J, Der Kiureghian A (2006) Generalized Bouc-Wen model for highly asymmetric hysteresis. J Eng Mech 132:610–618 Song J, Ellingwood BR (1999) Seismic reliability of special moment steel frames with welded connections: I. J Struct Eng 125:357–371 Song J, Der Kiureghian A, Sackman JL (2007) Seismic interaction in electrical substation equipment connected by non-linear rigid bus conductors. Earthquake Eng Struct Dyn 36:167–190 Soong TT (1998) Experimental simulation of degrading structures through active control. Earthquake Eng Struct Dyn 27:143–154 Soong TT, Constantinou MC (1994) Passive and active structural vibration control in civil engineering. Springer, Berlin Soong TT, Grigoriu M (1993) Random vibration of mechanical and structural systems. Prentice-Hall, New York Spanos PD, Cacciola P, Muscolino G (2004) Stochastic averaging of preisach hysteretic systems. J Eng Mech 130:1257–1267 Spencer BF, Suhardjo J, Sain MK (1994) Frequency domain optimal control strategies for aseismic protection. J Eng Mech 120:135–159 Spencer BF, Dyke SJ, Sain MK, Carson JD (1997) Phenomenological model for magnetorheological damper. J Eng Mech 123(3):230–238 Staudacher K (1982) Integral earthquake protection of structures iv: full base isolation and seismic mass analogy. Technical report, Eidgenossische Technische Hochschule (Zurich), Inst für Baustatikund Konstruktion, Bericht 134. Birkhäuser, Basel Stengel RF (1986) Stochastic optimal control: theory and application. Wiley, New York Sues RH, Mau ST, Wen YK (1988) System identification of degrading hysteretic restoring forces. J Eng Mech 114:833–846 Symans MD, Constantinou MC (1999) Semi-active control systems for seismic protection of structures: A state-of-the-art review. Eng Struct 21(6):469–487 Tan P, Dyke SJ, Richardson A, Abdullah M (2005) Integrated device placement and control design in civil structures using genetic algorithms. J Struct Eng 131(10):1489–1496 Thyagarajan RS (1989) Modeling and analysis of hysteretic structural behavior. Technical report, Rep No EERL 89-03, California Institute of Technology, Pasadena, Calif Thyagarajan RS, Iwan WD (1990) Performance characteristics of a widely used hysteretic model in structural dynamics. Technical report, Proc 4th US nat conf on earthquake engrg, vol 2, EERI, Oakland, Calif, pp 177–186 Tsang HH, Su RKL, Chandler AM (2006) Simplified inverse dynamics models for MR fluid dampers. Eng Struct 28(3):327–341 Tse T, Chang CC (2004) Shear-mode rotary magnetorheological damper for small-scale structural control experiments. J Struct Eng 130:904–911 Tyler RG, Robinson WH (1984) High-strain tests on lead-rubber bearings for earthquake loadings. Bull N Z Soc Earthq Eng 17:90–105 Uang CM, Bertero VV (1988) Use of energy as a design criterion in earthquake resistant design. Technical report, UCB/EERC-88/18, University of California, Berkeley Uang CM, Bertero VV (1990) Evaluation of seismic energy in structures. Earthquake Eng Struct Dyn 19:77–90 Unsal M, Crane CD, Niezrecki C (2006) Vibration control of parallel platforms based on magnetorheological damping. In: Florida conference on recent advances in robotics, FCRAR, Miami, Florida, 25–26 May 2006 Valanis KC (1971) A theory of viscoplasticity without a yield surface. Part i: General theory. Arch Mech 23(4):517–533 Van de Lindt JW (2004) Evolution of wood shear wall testing, modeling, and reliability analysis: bibliography. Pract Period Struct Des Constr 9(1):44–53 Van de Lindt JW, Rosowsky DV (2005) Strength-based reliability of wood shearwalls subject to wind load. J Struct Eng 131:359–363 Van de Lindt JW, Walz MA (2003) Development and application of wood shear wall reliability model. J Struct Eng 129:405–413 Vavreck AN (2000) Control of a dynamic vibration absorber with magnetorheological damping. Technical report, Pennsylvania State University, Altoona Collegue, Altoona, Pennsylvania Visintin A (1994) Differential models of hysteresis. Springer, Berlin Wang C, Foliente GC (2001) Hysteretic models for deteriorating inelastic structures. J Eng Mech 127:1200–1202 Wang DH, Liao WH (2005) Modeling and control of magnetorheological fluid dampers using neural networks. Smart Mater Struct 14:111–126 Wang CH, Wen YK (2000) Evaluation of pre-northridge low rise steel buildings. Part I: Modeling. J Eng Mech 126(10):1160–1168 Wang ER, Ma XQ, Rakheja S, Su CY (2004) Modeling asymmetric hysteretic properties of an mr fluids damper. In: 43rd IEEE conference on decision and control, Atlantis, Paradise Island, Bahamas, 14–17 December 2004 Warn GP, Whittaker AS (2004) Performance estimates in seismically isolated bridge structures. Eng Struct 26(9):1261–1278 Weea H, Kim YY, Jungb Hl, Leec GN (2001) Nonlinear rate-dependent stick-slip phenomena: Modeling and parameter estimation. Int J Solids Struct 38(8):1415–1431 Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(EM2):246–263 Wen YK (1980) Equivalent linearization for hysteretic systems under random excitation. J Appl Mech 47:150–154 Wen YK (1986) Stochastic response and damage analysis of inelastic structures. Probab Eng Mech 1(1):49–57 Wen YK (1989) Methods of random vibration for inelastic structures. Appl Mech Rev 42(2):39–52 Wentzel H (2006) Modelling of frictional joints in dynamically loaded structures—a review. Technical report, Dept of Solid Mechanics, Royal Institute of Technology (KTH) (SE-100 44 Stockholm) Sweden Whalen TM, Bhatia KM, Archer GC (2002) Semi-active vibration control for the 3rd generation benchmark problem including spillover suppression. In: 15th ASCE engineering mechanics conference, Columbia University, New York, 2–5 June 2002 Whittaker A, Constantinou M, Tsopelas P (1999) Nonlinear procedures for seismic evaluation of buildings. Struct Des Tall Build 8:1–13 Wilson EL (2002) Three-dimensional static and dynamic analysis of structures, 3rd edn. CSI, Computers and Structures, Berkeley Wong CW, Ni YQ, Ko JM (1994) Steady-state oscillation of a hysteretic differential model. Part II: Performance analysis. J Eng Mech 120:2299–2325 Wong CW, Ni YQ, Lau SL (1994) Steady-state oscillation of a hysteretic differential model. Part I: Response analysis. J Eng Mech 120(11):2271–2298 Wright FL (1977) An autobiography: Frank Lloyd Wright. Horizon Press, New York Xia PQ (2005) An inverse model of MR damper using optimal neural network and system identification. J Sound Vib 266:1009–1023 Xu Z, Agrawal AK, He WL, Tan P (2007) Performance of passive energy dissipation systems during near-field ground motion type pulses. Eng Struct 29:224–236 Yaghoubian J (1991) Isolating building contents from earthquake induced floor motions. Earthq Spectra 7(1):127–143 Yang JN, Agrawal AK (2002) Semi-active hybrid control systems for nonlinear buildings against near-field earthquakes. Eng Struct 24(3):271–280 Yang CY, Cheng HD, Roy RV (1991) Chaotic and stochastic dynamics for a nonlinear structural system with hysteresis and degradation. Probab Eng Mech 6(3–4):193–203 Yang JN, Wu JC, Agrawal AK (1995) Sliding mode control for nonlinear and hysteretic structures. J Eng Mech Div 21(12):1330–1339 Yang JN, Kim JH, Agrawal AK (2000) A resetting semi-active stiffness damper for seismic response control. J Struct Eng 126(12):1427–1433 Yang G, Spencer BF, Carlson JD, Sain MK (2002) Large-scale MR fluid dampers: modeling and dynamic performance considerations. Eng Struct 24:309–323 Yang G, Spencer BF, Jung HJ, Carlson JD (2004) Dynamic modeling of large-scale magnetorheological damper systems for civil engineering applications. J Eng Mech 130(9):1107–1114 Yao GZ, Yap FF, Chen G, Li WH, Yeo SH (2002) MR damper and its application for semi-active control of vehicle suspension system. Mechatronics 12:963–973 Yar M, Hammond JK (1987) Parameter estimation for hysteretic systems. J Sound Vib 117:161–172 Yi F, Dyke SJ, Frech S, Carlson JD (1998) Investigation of magnetorheological dampers for earthquake hazard mitigation. In: Proc 2nd world conf on struct control. Wiley, New York, pp 349–358 Yi F, Dyke SJ, Caicedo JM, Carlson JD (1999) Seismic response control using smart dampers. In: Proc Am control conf American automatic control council, Washington, pp 1022–1026 Yi F, Dyke SJ, Caicedo JM, Carlson. JD (2001) Experimental verification of multiinput seismic control strategies for smart dampers. J Eng Mech 127(11):1152–1164 Ying ZG, Zhu WQ, Ni YQ, Ko JM (2002) Stochastic averaging of Duhem hysteretic systems. J Sound Vib 254(1):91–104 Yong P (1981) Parameter estimation for continuous time models-a survey. Automatica 17:23–39 Yosef SS, Bruce AB (1994) Optimization by pattern search. Eur J Oper Res 78:277–303 Yoshida O, Dyke SJ (2004) Seismic control of a nonlinear benchmark building using smart dampers. J Eng Mech 130:386–392 Yoshida O, Dyke SJ (2005) Response control of full scale irregular buildings using MR dampers. J Struct Eng 131(5):734–742 Yoshida O, Dyke SJ, Giacosa LM, Truman KZ (2002) Torsional response control of asymmetric buildings using smart dampers. In: 15th ASCE engineering mechanics conference, Columbia University, New York, 2–5 June 2002 Yoshioka H, Ramallo JC, Spencer BF (2002) Smart base isolation strategies employing magnetorheological dampers. J Eng Mech 128:540–551 Younis CJ, Tadjbakhsh IG (1984) Response of sliding rigid structure to base excitation. J Eng Mech 110:417–32 Yu G, Lin W, Hong R (2006) Fuzzy control of piezoelectric systems using relaxed lmi stability conditions. In: Proceedings of 2006 CACS automatic control conference, St John’s University, Tamsui, Taiwan, 10–11 November 2006 Zaiming L, Katukura H (1990) Markovian hysteretic characteristics of structures. J Eng Mech 116(8):1798–1811 Zayas VA, Low SS, Mahin SA (1990) A simple pendulum technique for achieving seismic isolation. Earthq Spectra 6:317–333 Zhang H, Foliente GC, Yang Y, Ma F (2002) Parameter identification of inelastic structures under dynamic loads. Earthquake Eng Struct Dyn 31:1113–1130 Zhang J, Makris N, Delis T (2004) Structural characterization of modern highway overcrossings-case study. J Struct Eng 130:846–860 Zhang J, Sato T, Iai S (2007) Non-linear system identification of the versatile-typed structures by a novel signal processing technique. Earthquake Eng Struct Dyn 36:909–925 Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice-Hall, New York Zhou Q, Nielsen SRK, Qu WL (2006) Semi-active control of three-dimensional vibrations of an inclined sag cable with magnetorheological dampers. J Sound Vib 296:1–22 Zhu WQ, Lin YK (1991) Stochastic averaging of energy envelope. J Eng Mech 117:1890–1905 Zhu WQ, Luo M, Dong L (2004) Semi-active control of wind excited building structures using MR/ER dampers. Probab Eng Mech 19(3):279–285 Zwillinger D (2003) CRC, standard mathematical tables and formulae, 31st edn. CRC Press, Boca Raton