Mathematical Model for Design of Mass Dampers for Wind Excited Structures
Publication: Journal of Engineering Mechanics
Volume 128, Issue 9
Abstract
A state space linear mathematical model oriented to the design of passive and active mass dampers for tall buildings and bridges subjected to the wind action is presented in this paper. The model accounts for an arbitrary number of passive and/or active damping devices positioned at arbitrary points of the structure, as well as for an arbitrary number of structural modes of vibration. The aerodynamic terms of the stiffness and damping matrices are considered following a linearized quasisteady approach. A general discussion on the application of control techniques to the synthesis of the active mass dampers control law is carried out. For the tuning of the mechanical parameters of passive devices, the problem is reformulated in terms of a decentralized static output feedback control law design problem.
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References
Ankireddi, S., and Yang, H. T. Y.(1996). “Simple ATMD control methodology for tall buildings subject to wind loads.” J. Struct. Eng., 122(1), 83–91.
Davenport, A. G.(1967). “Gust loading factors.” J. Struct. Div., Am. Soc. Civ. Eng., 93(3), 11–34.
Davis, M. C.(1963). “Factoring the spectral matrix.” IEEE Trans. Autom. Control, AC-8, 296–304.
Doyle, J. C., Glover, K., Khargonekar, P. P., and Francis, B. A.(1989). “State space solutions to the standard and problems.” IEEE Trans. Autom. Control, AC-34, 831–847.
Doyle, J. C., Packard, A., and Zhou, K. (1986). “Review of LFTs, LMIs, and μ,” Proc., 30th IEEE Conf. Decision and Control, Brighton, U.K., 1227–1232.
El Ghaoui, L., and Balakrishnan, V. (1994). “Synthesis of fixed structure controllers via numerical optimisation.” Proc., 33rd Conf. on Decision and Control, Lake Buena Vista, Fla., 2678–2683.
Großmann, E., and Waller, H.(1983). “Analysis of multicorrelated wind-excited vibrations of structures using the covariance method.” Eng. Struct., 5, 264–272.
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, B. F., and Jao, J. T. P.(1997). “Structural Control: Past, Present and Future.” J. Eng. Mech., 123(9), 897–971.
Hrovat, D., Barak, P., and Rabins, M.(1983). “Semiactive versus passive or active tuned mass dampers for structural control.” J. Eng. Mech., 109(3), 691–705.
Hyland, D. C., and Bernstein, D. S.(1984). “The optimal projection equations for fixed-order dynamic compensation.” IEEE Trans. Autom. Control, 29(11), 1034–1037.
Iwasaki, T., and Skelton, R. E.(1995). “All fixed order controllers: Observer-based structure and covariance bounds.” IEEE Trans. Autom. Control, 40, 512–516.
Kailath, T., (1980). Linear systems, Prentice-Hall, London.
Kareem, A., Kijewski, T., and Tamura, Y.(1999). “Mitigation of motions of tall buildings with specific examples of recent applications.” Wind Struct., 2(3), 201–251.
Luft, R. W.(1979). “Optimal tuned mass dampers for buildings.” J. Struct. Div., Am. Soc. Civ. Eng., 105(12), 2766–2772.
Mattei, M.(2000). “Sufficient Conditions for the synthesis of H-infinity fixed order controllers.” Int. J. Robust Nonlinear Control, 10(15), 1237–1248.
McNamara, R. J.(1977). “Tuned mass dampers for buildings.” J. Struct. Div., Am. Soc. Civ. Eng., 103(9), 1785–1798.
Miyata, T., Yamada, H., Dung, N. N., and Kazama, K. (1994). “On active control and structural response control of the coupled flutter problem for long span bridges.” Proc., 1st World Conf. on Structural Control, Los Angeles, WA4, 13–22.
Nishitani, A., and Yamada, N. (1994). “H-infinity structural response control with reduced order controller.” Proc., 1st World Conf. on Structural Control, Los Angeles, TP4, 100–109.
Ricciardelli, F. (1996). “Risposta delle torri di ponti di grande luce all’azione del vento.” PhD thesis, Università di Napoli Federico II, Napoli, Italy (in Italian).
Ricciardelli, F.(1999). “A linear model for structures with tuned mass dampers.” Wind Struct., 2(3), 151–171.
Sakamoto, M., Kobori, T., Yamada, T., and Takahashi, M. (1994). “Practical applications of active and hybrid response control systems and their verifications by earthquake and strong wind observations.” Proc., 1st World Conf. Structural Control, Los Angeles, WP2, 90–99.
Simiu, E., and Scanlan, R. H. (1996). Wind effects on structures, 3rd Ed. Wiley, New York.
Solari, G. (1994). “Gust excited-vibrations.” Wind-excited vibrations of structures, H. Sockel, ed., Springer-Verlag, Berlin.
Spencer, B. F., and Sain, M. K.(1997). “Controlling buildings: A new frontier of feedback.” IEEE Control Syst. Mag., 17, 19–35.
Suhardjo, J., Spencer, B. F., Jr., and Kareem, A.(1992a). “Frequency domain optimal control of wind excited buildings” J. Eng. Mech., 118(12), 2463–2481.
Suhardjo, J., Spencer, B. F., Jr., and Kareem, A.(1992b). “Active control of wind excited buildings: a frequency domain based design approach.” J. Wind. Eng. Ind. Aerodyn., 41, 1985–1996.
Vickery, B. J. (1970). “On the reliability of gust loading factors.” Technical Meeting on Wind Loads on Buildings and Structures, Building Science Series No. 30, National Bureau of Standards, Washington, D.C.
Vickery, B. J., and Clark, A. W.(1972). “Lift or across-wind response to tapered stacks.” J. Struct. Div., Am. Soc. Civ. Eng., 98(1), 1–20.
Warburton, G. B.(1982). “Optimum absorber parameters for various combination of response and excitation parameters.” Earthquake Eng. Struct. Dyn., 10, 381–401.
Yoshida, K., and Watanabe, T. (1994). “Robust control of structural vibrations using active dynamic vibration absorber systems.” Proc., 1st World Conf. on Structural Control, Los Angeles, TP4, 53–62.
Zhou, K., Doyle, J. C., and Glover, K. (1995). Robust and optimal control, Prentice-Hall, London.
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Published In
Journal of Engineering Mechanics
Volume 128 • Issue 9 • September 2002
Pages: 979 - 988
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Jul 11, 2000
Accepted: Jul 20, 2001
Published online: Aug 15, 2002
Published in print: Sep 2002
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