Seismic Analysis and Design with Maxwell Dampers
Publication: Journal of Engineering Mechanics
Volume 129, Issue 3
Abstract
The paper presents a convenient formulation for the optimal design of viscous dampers, represented by a Maxwell model. The Maxwell model captures the frequency dependence of the damping and stiffness coefficients observed in the fluid orifice dampers, especially at higher frequencies of deformation. A gradient-based optimization scheme is used to obtain the optimal distribution and the parameters of the dampers in a structure subjected to seismic motions. Since the objective of using supplemental damping is to reduce the dynamic response, the optimal solution aims to minimize a response-based performance index. Different forms of the performance indices are considered to obtain the numerical results. The effectiveness of supplemental damping is evaluated in terms of the reduction of the response quantities such as base shear, story drifts, story accelerations, and floor response spectra. The effect of spring in the Maxwell model as well as that of the brace flexibility is also examined. Both tend to reduce the effectiveness of the viscous dampers.
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References
Constantinou, M. C., Soong, T. T., and Dargush, G. F. (1998). “Passive energy dissipation systems for structural design and retrofit.” Monograph No. 1, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, N.Y.
Constantinou, M. C., and Symans, M. D.(1993). “Seismic response of structures with supplemental damping.” Struct. Des. Tall Build., 2, 93–132.
Fox, R. L., and Kapoor, M. P.(1968). “Rates of change of eigenvalues and eigenvectors.” AIAA J., 6(12), 2426–2429.
Ghafory-Ashtiany, M., and Singh, M. P. (1981). “Seismic response of structural system with random parameters.” Rep. No. VPI-E81.15, Virginia Polytechnic Institute and State Univ., Blacksburg, Va.
Haftka, R. T., and Gürdal, Z. (1992). Elements of structural optimization, Kluwer Academic, Dordrecht, the Netherlands.
Hanson, R.(1993). “Supplemental damping for improved seismic performance.” Earthquake Spectra, 9(3), 319–334.
Igusa, T., Kiureghian, A. D., and Sackman, J. L.(1984). “Modal decomposition method for stationary response of non-classically damped systems.” Earthquake Eng. Struct. Dyn., 14, 133–146.
Kanai, K.(1961). “An empirical formula for the spectrum of strong earthquake motions.” Bull. Earthquake Res. Inst., Univ. Tokyo, 39, 85–95.
Makris, N., and Constantinou, M. C.(1991). “Fractional derivative model for viscous dampers.” J. Struct. Eng., 117(9), 2708–2724.
Maldonado, G. O., and Singh, M. P.(1991). “An improved response spectrum method for calculating seismic design response. Part II: Non-classically damped structures.” Earthquake Eng. Struct. Dyn., 20(7), 637–649.
Moreschi, L. (2000). “Seismic design of energy dissipation systems for optimal structural performance.” PhD dissertation, Engineering Science & Mechanics, Virginia Tech, Blacksburgh, Va.
Murthy, D. V., and Haftka, R. T.(1988). “Derivatives of eigenvalues and eigenvectors of a general complex matrix.” Int. J. Numer. Methods Eng., 26, 293–311.
Rao, S. S. (1996). Engineering optimization, Wiley, New York.
Reinhorn, A. M., Li, C., and Constantinou, M. C. (1995). “Experimental and analytical investigation of seismic retrofit of structures with supplemental damping: Part 1—fluid viscous damping devices.” Report No. NCEER 95-0001, National Center for Earthquake Engineering Research, Univ. of New York at Buffalo, Buffalo, N.Y.
Rosen, J. B. (1960). “The gradient projection method for nonlinear programming, Part I: Linear constraints.” Society of Industrial and App. Mathematics, J. Appl. Math., 8, 181–217.
Singh, M. P.(1980). “Seismic response by SRSS for Nonproportional damping.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 106(6), 1405–1419.
Singh, M. P., Chang, T. S., and Suárez, L. E.(1992). “A response spectrum method for seismic design evaluation of rotating machines.” J. Vibr. Acoust., 114, 454–460.
Singh, M. P., and Moreschi, L. M. (1999). “Genetic algorithm-based control of structures for dynamic loads.” IA’99 Proc., International Seminar on Numerical Analysis in Solid and Fluid Dynamics in 1999, E. Tachibana and Y. Mukai, eds., Osaka Univ., Osaka, Japan, 277–284.
Soong, T. T., and Dargush, G. F. (1997). Passive energy dissipation systems in structural engineering, Wiley, New York.
Tajimi, H. (1960). “A statistical method of determining the maximum response of a building structure during an earthquake.” Proc., II World Conf. in Earthquake Engineering, Tokyo, 781–797.
Verma, N. P. (2001). “Viscous dampers for optimal reduction in seismic response.” MS thesis, Virginia Polytechnic Institute and State Univ., Blacksburg, Va.
Zhang, R. H., and Soong, T. T.(1992). “Seismic design of viscoelastic dampers for structural applications.” J. Struct. Eng., 118(5), 1375–1392.
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Published In
Journal of Engineering Mechanics
Volume 129 • Issue 3 • March 2003
Pages: 273 - 282
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Aug 9, 2001
Accepted: Mar 29, 2002
Published online: Feb 14, 2003
Published in print: Mar 2003
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