Dimensional Analysis of Inelastic Structures with Negative Stiffness and Supplemental Damping Devices
Publication: Journal of Structural Engineering
Volume 143, Issue 3
Abstract
A negative stiffness device (NSD) has been proposed as an innovative way for seismic protection of structures. It was shown both numerically and experimentally to improve the performance of inelastic structures when it is appropriately designed for the given application. In order to systematically evaluate the effects of a NSD, dimensional analysis is used in this study to quantify the structural responses as the function of input ground motion characteristics, model parameters of structure and NSD, as well as supplemental damping. To facilitate this, a simplified yet parameterized numerical model is first proposed to mimic the observed responses of the tested prototype NSD. The dimensional analysis is then conducted on a single degree of freedom (SDOF) system equipped with both a NSD and a nonlinear damper. By comparing the dimensionless structural responses for the cases of (1) inelastic structure only, (2) inelastic structure with nonlinear damper, and (3) inelastic structure with both nonlinear damper and NSD when subject to various pulse type motions, the effectiveness of a NSD is investigated thoroughly. Finally, the optimal ranges of NSD model parameters are also identified.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was partially funded by the National Science Foundation under the grant CMMI-0830391, Joy Pauschke, program manager. The authors also would like to thank other members of the project team for their help and intellectual exchange, in particular Dr. Pasala Dharma Theja from Rice University, Dr. Sarlis Apostolos, Professor Reinhorn Andrei, and Professor Constantinou Michael from State University of New York (SUNY), Buffalo, New York.
References
Attary, N., et al. (2015). “Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection.” Earthquake Eng. Struct. Dyn., 44(6), 973–995.
Iemura, H., Igarashi, A., Pradono, M. H., and Kalantari, A. (2006). “Negative stiffness friction damping for seismically isolated structures.” J. Struct. Control Health, 13(2-3), 775–791.
Lee, C.-M., Goverdovskiy, V. N., and Temnikov, A. I. (2007). “Design of springs with ‘negative’ stiffness to improve vehicle driver vibration isolation.” J. Sound Vib., 302(4-5), 865–874.
Makris, N. (2014). “A half-century of rocking isolation.” Earthquakes Struct., 7(6), 1187–1221.
Makris, N., and Black, C. J. (2004a). “Dimensional analysis of bilinear oscillators under pulse-type excitations.” J. Eng. Mech., 1019–1031.
Makris, N., and Black, C. J. (2004b). “Evaluation of peak ground velocity as a ‘good’ intensity measure for near-source ground motions.” J. Eng. Mech., 1032–1044.
Makris, N., and Chang, S. (2000). “Effect of viscous, visco-plastic and friction damping on the response of seismic isolated structures.” Earthquake Eng. Struct. Dyn., 29(1), 85–107.
Naeim, F., and Kelly, J. M. (1999). Design of seismic isolated structures: From theory to practice, Wiley, New York.
Nagarajaiah, S., Reinhorn, A. M., Constantinou, M. C., Taylor, D., Pasala, D. T. R., and Sarlis, A. A. (2010). “True adaptive negative stiffness: A new structural modification approach for seismic protection.” Proc., 5th World Conf. on Structural Control and Monitoring, Int. Association of Structural Control and Monitoring, Univ. of Southern California, Los Angeles.
Pasala, D. T. R., Sarlis, A. A., Nagarajaiah, S., Reinhorn, A. M., Constantinou, M. C., and Taylor, D. (2013). “Adaptive negative stiffness: A new structural modification approach for seismic protection.” J. Struct. Eng., 1112–1123.
Pasala, D. T. R., Sarlis, A. A., Reinhorn, A. M., Nagarajaiah, S., Constantinou, M. C., and Taylor, D. (2014). “Simulated bilinear-elastic behavior in a SDOF elastic structure using negative stiffness device: Experimental and analytical study.” J. Struct. Eng., 04013049.
Pasala, D. T. R., Sarlis, A. A., Reinhorn, A. M., Nagarajaiah, S., Constantinou, M. C., and Taylor, D. (2015). “Apparent-weakening in SDOF yielding structure using negative stiffness device: Experimental and analytical study.” J. Struct. Eng., 04014130.
Reinhorn, A. M., Viti, S., and Cimellaro, G. P. (2005). “Retrofit of structures: Strength reduction with damping enhancement.” Proc., 37th UJNR Panel Meeting on Wind and Seismic Effects, Public Works Research Institute, Tsukuba-shi, Japan, 16–21.
Sarlis, A. A., Pasala, D. T. R., Constantinou, M. C., Reinhorn, A. M., Nagarajaiah, S., and Taylor, D. (2013). “Negative stiffness device for seismic protection of structures.” J. Struct. Eng., 1124–1133.
Soong, T. T., and Spencer, B. F. (2002). “Supplemental energy dissipation: State-of-the-art and state-of-the-practice.” Eng. Struct., 24(3), 243–259.
Spencer, B. F., and Nagarajaiah, S. (2003). “State of the art of structural control.” J. Struct. Eng., 845–856.
Symans, M. D., et al. (2008). “Energy dissipation systems for seismic applications: Current practice and recent developments.” J. Struct. Eng., 3–21.
Viti, S., Cimellaro, G. P., and Reinhorn, A. M. (2006). “Retrofit of a hospital through strength reduction and enhanced damping.” Smart Struct. Syst., 2(4), 339–355.
Zhang, J., and Tang, Y. (2009). “Dimensional analysis of structures with translating and rocking foundations under near-fault ground motions.” Soil Dyn. Earthquake Eng., 29(10), 1330–1346.
Zhang, J., and Xi, W. (2012). “Optimal nonlinear damping for inelastic structures using dimensional analysis.” Structures Congress, Structural Engineering Institute, Reston, VA.
Zhang, J., Xu, S., and Tang, Y. (2011). “Inelastic displacement demand of bridge columns considering shear-flexure interaction.” Earthquake Eng. Struct. Dyn., 40(7), 731–748.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 143 • Issue 3 • March 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 3, 2016
Accepted: Jul 25, 2016
Published online: Sep 27, 2016
Discussion open until: Feb 27, 2017
Published in print: Mar 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.