Designing Variable Stiffness Semi-Active Tuned Mass Damper for Nonlinear Structures

Document Type : Research Article

Authors

Engineering Department , University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

In this paper, designing variable stiffness semi-active tuned mass damper (SATMD) for
mitigating the responses of nonlinear structures under earthquake excitation has been studied. Two semiactive control algorithms based on instantaneous optimal control and clipping control concept as well as
modified balance control have been developed to determine the optimal stiffness of SATMD for nonlinear
structures in each time step. For determining optimal parameters of semi-active control system including
the weighting matrices in performance index of control algorithm as well as the maximum and minimum
values of SATMD stiffness, an optimization problem for minimization of structure maximum response has
been defined where genetic algorithm (GA) has been used for optimization. For numerical simulations, an
eight-story nonlinear shear building with bilinear hysteresis behavior has been subjected to a white noise
excitation and optimal SATMDs have been designed. The results showed that optimal variable stiffness
SATMD using both control algorithms has been effective in suppressing the seismic responses of nonlinear
structure. Also, variable stiffness SATMD shows better performance than TMD and variable damping
SATMD in structural response controlling. Comparing the performance of the variable stiffness SATMD
under testing earthquakes which were different from design record, showed that the efficiency of SATMD
depends on the characteristics of excitation, hence design record needs to be chosen properly.

Keywords

Main Subjects


[1] Spencer, B.F., Nagarajaiah, S., “State of the Art of Structural Control”, J. Struct. Eng., ASCE, 129 (2003) pp. 845-856.
[2] Warburton, G.B., “Optimal Absorber Parameters for Various Combination of Response and Excitation Parameters”, Earthquake Engineering and Structural Dynamics, 10 (1982) pp. 381-401.
[3] Chang, J.C.H., Soong, T.T., “Structural control using active tuned mass dampers”, Journal of Engineering Mechanics, ASCE, 6 (1980) pp. 1091-1098.
[4] Ikeda, Y., Sasaki, K., Sakamoto, M., Kobori, T.,“Active mass driver system as the first application of active structural control”, Earthquake Engineering and Structural Dynamics, 30 (2001) pp. 1575-1595.
[5] Sun, J.Q., Jolly, M.R., Norris, M.A., “Passive, adaptive, and active tuned vibration absorber - A survey”, Journal of Mechanical Design, 117 (1995) pp. 234-242.
[6] Hrovat, D., Barak, P., Rabins, M., “Semi-active versus passive or active tuned mass dampers for structural control”, Journal of Engineering Mechanics, ASCE, 109 (1983) pp. 691-705.
[7] Abe, M., “Semi-active tuned mass dampers for seismic protection of civil structures”, Earthquake Engineering and Structural Dynamics, 25 (1996) pp. 743-749.
[8] Abe, M., Igusa, T., “Semi-active dynamic vibration absorbers for controlling transient response”, Journal of Sound and Vibration, 198 (1996) pp. 547-569.
[9] Kobori, T., Takahashi, M., “Seismic response controlled structure with active variable stiffness system”, Earthquake Engineering and Structural Dynamics, 22 (1993) pp. 925-941.
[10] Bobrow, J., Jabbari, F., Thai, K., “A new approach to shock isolation and vibration suppression using a resettable actuator”, Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 122 (2000) pp. 570-573.
[11] Yang, J.N., Kim, J.H., Agrawal, A.K., “Resetting semiactive stiffness damper for seismic response control”, Journal of Structural Engineering, ASCE, 126 (2000) pp. 1427-1433.
[12] Nagarajaiah, S., Mate, D., “Semiactive control of continuously variable stiffness system”, Proc., 2nd World Conf. Struct. Control, 1 (1998) pp. 397-405.
[13] Nagarajaiah, S., Varadarajan, N., “Novel semiactive  variable stiffness tuned mass damper with real time tuning capacity”, Proc., 13th Engineering Mechanics Conf. ASCE, Reston, Va, 2000.
[14] Varadarajan, N., Nagarajaiah, S., “Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/Hilbert transform”, Journal of Engineering Mechanics, ASCE, 130 (2004) pp. 451-458.
[15] Nagarajaiah, S., Varadarajan, N., “Short time Fourier transform algorithm for wind response control of buildings with variable stiffness tmd”, Engineering Structures, 27 (2005) pp. 431-441.
[16] Nagarajaiah, S., Sonmez, E., “Structures of semiactive variable stiffness multiple tuned mass dampers under harmonic forces”, Journal of Structural Engineering,ASCE, 133 (2007) pp. 67-77.
[17] Nagarajaiah, S., “Adaptive passive, semiactive, smart tuned mass dampers: identification and control using empirical mode decomposition, Hilbert transform, and short-term Fourier transform”, Structural Control and Health Monitoring, 16 (2009) pp. 800–841.
[18] Sun, C., Eason, R.P., Nagarajaiah, S., Dick, A.J.,“Hardening Düffing oscillator attenuation using a nonlinear TMD a semi-active TMD and a multiple TMD”,Journal of Sound and Vibration, 332 (2013) pp. 674-686.
[19] Eason, R.P., Sun, C., Nagarajaiah, S., Dick, A.J.,“Attenuation of a linear oscillator using a nonlinear and a semi-active tuned mass damper in series”, Journal of Sound and Vibration, 332 (2013) pp. 154-166.
[20] Sun, C., Nagarajaiah, S., “Study on semi-active tuned mass damper with variable damping and stiffness under seismic excitations”, Structural Control and Health Monitoring, 21 (2014) pp. 890-906.
[21] Dyke, S.J., Spencer, B.F., Sain, M.K., Carlson, J.D.,“Modeling and control of magnetorheological dampers for seismic response reduction”, Smart Materials and Structures, 5 (1996) pp. 565-575.
[22] Pinkaew, T., Fujino, Y., “Effectiveness of Semi-Active Tuned Mass Dampers under Harmonic Excitation”, Engineering Structures, 23 (2001) pp. 850-856.
[23] Ji, H., Moon, Y., Kim, C., Lee, I., “Structural vibration control using semi-active tuned mass damper”, Proc Eighteenth KKCNN Symposium on Civil Engineering KAIST6, Taiwan, 2005.
[24] Chang, C.C., Yang, H.T.Y., “Instantaneous optimal control of building frames”, Journal of Structural Engineering, ASCE, 120 (1994) pp. 1307-1326.
[25] Joghataie, A., Mohebbi, M., “Vibration controller design for confined masonry walls by distributed genetic algorithms”, Journal of Structural Engineering, ASCE, 134 (2008) pp. 300-309.
[26] Sireteanu, T., Stancioiu, D., Stammers, C.W., “Use of magnetorheological fluid dampers in semi-active driver seat vibration control”, ACTIVE 2002, ISVR,Southampton, UK, 2002.
[27] Dyke, S.J., Spencer, B.F., “A comparison of semi-active control strategies for the MR damper”, Proceedings of International Conference on Intelligent Information Systems, Bahamas, 1997.
[28] Carter, A.K., “Transient motion control of passive and semiactive damping for vehicle suspensions”, Master of science thesis in electrical engineering, University of Virginia, 1998.
[29] Francois, A., Man, P.D., Bossens, F., Preumont, A.,“State of the art of MR fluids technology and semiactive control”, orkpackage No. 1, Universite Libre de Bruxelles, Brussels, Belgium. CaSCo- Consistent Semiactive System Control. 2000.
[30] Bathe, K.J., “Finite element Procedures”, New Jersey:Prentice-Hall, Inc, 1996.
[31] Goldberg, D.E., “Genetic algorithms in search,optimization and machine learning”, Addison-Wesley Publishing Co., Inc. Reading, Mass, 1989.
[32] Hadi, N.S., Arfiadi, Y., “Optimum design of absorber for MDOF structures”, ASCE Journal of Structural Engineering, 124 (1998) pp. 1272-1280.
[33] Mohebbi, M. Joghataie, A., “Designing optimal tuned mass dampers for nonlinear frames by distributed genetic algorithms”, The Structural Design of Tall and Special Buildings, 21 (2011) pp. 57-76.
[34] Yang, J.N., Long, F.X., Wong, D., “Optimal control of nonlinear flexible structures”, Journal of Applied Mechanics, ASME, 55 (1988) pp. 931-938.