Modeling, Characterizing, and Testing a Simple, Smooth Negative-Stiffness Device to Achieve Apparent Weakening
Publication: Journal of Engineering Mechanics
Volume 146, Issue 10
Abstract
Apparent weakening is the softening of a structure’s apparent stiffness by adding negative stiffness to the overall system, which has the benefit of reducing the peak accelerations and base shears induced in the structure due to a seismic event. Apparent weakening is an elastic effect that does not reduce the main structural strength. To attain this behavior, negative stiffness can be introduced through the integration of negative stiffness devices. This study presents a novel smooth negative stiffness device (SNSD) consisting of cables, pulleys, and tension springs. A nonlinear mathematical model of the force-deflection behavior of the SNSD was developed and used to determine the optimal geometry for such a device. A prototype device was designed and fabricated for installation in a bench-scale experimental structure, which was characterized through static and dynamic tests. This paper also presents a numerical study on two other device configurations designed to achieve different force-deflection relations for use in an inelastic model building subject to a suite of historic and synthetic ground motions. In both the experimental prototype and the numerical study, the SNSDs successfully produced apparent weakening, effectively reducing accelerations and base shears of the structures.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. NSF-CMMI-1663376. This support is greatly appreciated.
References
Attary, N., M. Symans, and S. Nagarajaiah. 2017. “Development of a rotation-based negative stiffness device for seismic protection of structures.” J. Vib. Control 23 (5): 853–867. https://doi.org/10.1177/1077546315585435.
Attary, N., M. Symans, S. Nagarajaiah, A. M. Reinhorn, M. C. Constantinou, A. A. Sarlis, D. T. R. Pasala, and D. Taylor. 2015a. “Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection.” Earthquake Eng. Struct. Dyn. 44 (6): 973–995. https://doi.org/10.1002/eqe.2495.
Attary, N., M. Symans, S. Nagarajaiah, A. M. Reinhorn, M. C. Constantinou, A. A. Sarlis, D. T. R. Pasala, and D. Taylor. 2015b. “Performance evaluation of negative stiffness devices for seismic response control of bridge structures via experimental shake table tests.” J. Earthquake Eng. 19 (2): 249–276. https://doi.org/10.1080/13632469.2014.962672.
Attary, N., M. Symans, S. Nagarajaiah, A. M. Reinhorn, M. C. Constantinou, A. A. Sarlis, D. T. R. Pasala, and D. P. Taylor. 2015c. “Experimental shake table testing of an adaptive passive negative stiffness device within a highway bridge model.” Earthquake Spectra 31 (4): 2163–2194. https://doi.org/10.1193/101913EQS273M.
Chen, L., L. Sun, and S. Nagarajaiah. 2015. “Cable with discrete negative stiffness device and viscous damper: Passive realization and general characteristics.” Smart Struct. Syst. 15 (3): 627–643. https://doi.org/10.12989/sss.2015.15.3.627.
Cimellaro, G. P., M. Domaneschi, and G. Warn. 2018. “Three-dimensional base isolation using vertical negative stiffness devices.” J. Earthquake Eng. 1–29. https://doi.org/10.1080/13632469.2018.1493004.
Gavin, H. P. 2017. “The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems.” Accessed December 30, 2019. http://people.duke.edu/~hpgavin/lm.pdf.
Gavin, H. P., and B. W. Dickinson. 2011. “Generation of uniform-hazard earthquake ground motions.” J. Struct. Eng. 137 (3): 423–432. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000331.
Gong, W., and S. Xiong. 2017. “A new filter-based pseudo-negative-stiffness control for base-isolated buildings.” Struct. Control Health Monit. 24 (5): e1912. https://doi.org/10.1002/stc.1912.
Harvey, P. S. Jr, H. P. Gavin, and J. T. Scruggs. 2012. “Optimal performance of constrained control systems.” J. Smart Mater. Struct. 21 (8): 085001. https://doi.org/10.1088/0964-1726/21/8/085001.
Iemura, H., A. Igarashi, M. H. Pradono, and A. Kalantari. 2006. “Negative stiffness friction damping for seismically isolated structures.” Struct. Control Health Monit. 13 (2–3): 775–791. https://doi.org/10.1002/stc.111.
Iemura, H., and M. H. Pradono. 2002. “Passive and semi-active seismic response control of a cable-stayed bridge.” J. Struct. Control 9 (3): 189–204. https://doi.org/10.1002/stc.12.
Iemura, H., and M. H. Pradono. 2003. “Application of pseudo-negative stiffness control to the benchmark cable-stayed bridge.” J. Struct. Control 10 (3–4): 187–203. https://doi.org/10.1002/stc.25.
Iemura, H., A. Toyooka, M. Higuchi, and O. Kouchiyama. 2011. “Development of negative stiffness dampers for seismic protection.” Appl. Mech. Mater. 82: 645–650. https://doi.org/10.4028/www.scientific.net/AMM.82.645.
Ikago, K., K. Saito, and N. Inoue. 2012. “Seismic control of single-degree-of-freedom structure using tuned viscous mass damper.” Earthquake Eng. Struct. Dyn. 41 (3): 453–474. https://doi.org/10.1002/eqe.1138.
Kwon, I. Y., H. T. Yang, P. K. Hansma, and C. J. Randall. 2016. “Implementable bio-inspired passive negative spring actuator for full-scale structural control under seismic excitation.” J. Struct. Eng. 142 (1): 04015079. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001323.
Levenberg, K. A. 1944. “A method for the solution of certain non-linear problems in least squares.” Q. Appl. Math. 2 (2): 164–168. https://doi.org/10.1090/qam/10666.
Luo, H., K. Ikago, C. Chong, A. Keivan, and B. M. Phillips. 2019. “Performance of low-frequency structures incorporated with rate-independent linear damping.” Eng. Struct. 181 (Feb): 324–335. https://doi.org/10.1016/j.engstruct.2018.12.022.
Makris, N., and G. Kampas. 2016. “Seismic protection of structures with supplemental rotational inertia.” J. Eng. Mech. 142 (11): 04016089. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001152.
Nagarajaiah, S., A. M. Reinhorn, M. C. Constantinou, D. Taylor, D. T. R. Pasala, and A. A. S. Sarlis. 2010. “Adaptive negative stiffness: A new structural modification approach for seismic protection.” In Proc., 5th World Conf. on Structural Control and Monitoring. London: IASCM.
Pasala, D. T. R., A. A. Sarlis, S. Nagarajaiah, A. M. Reinhorn, M. C. Constantinou, and D. Taylor. 2013. “Adaptive negative stiffness: New structural modification approach for seismic protection.” J. Struct. Eng. 139 (7): 1112–1123. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000615.
Pasala, D. T. R., A. A. Sarlis, A. M. Reinhorn, S. Nagarajaiah, M. C. Constantinou, and D. Taylor. 2014. “Simulated bilinear-elastic behavior in a SDOF elastic structure using negative stiffness device: Experimental and analytical study.” J. Struct. Eng. 140 (2): 04013049. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000830.
Pasala, D. T. R., A. A. Sarlis, A. M. Reinhorn, S. Nagarajaiah, M. C. Constantinou, and D. Taylor. 2015. “Apparent weakening in SDOF yielding structures using a negative stiffness device: Experimental and analytical study.” J. Struct. Eng. 141 (4): 04014130. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001077.
Porter, J. H., T. M. Cain, S. L. Fox, and P. S. Harvey Jr. 2019. “Influence of infill properties on flexural rigidity of 3D-printed structural members.” Virtual Phys. Prototyp. 14 (2): 148–159. https://doi.org/10.1080/17452759.2018.1537064.
Pradono, M. H., H. Iemura, A. Igarashi, A. Toyooka, and A. Kalantari. 2009. “Passively controlled MR damper in the benchmark structural control problem for seismically excited highway bridge.” Struct. Control Health Monit. 16 (6): 626–638. https://doi.org/10.1002/stc.341.
Sarlis, A. A., D. T. R. Pasala, M. C. Constantinou, A. M. Reinhorn, S. Nagarajaiah, and D. P. Taylor. 2013. “Negative stiffness device for seismic protection of structures.” J. Struct. Eng. 139 (7): 1124–1133. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000616.
Sarlis, A. A., D. T. R. Pasala, M. C. Constantinou, A. M. Reinhorn, S. Nagarajaiah, and D. P. Taylor. 2016. “Negative stiffness device for seismic protection of structures: Shake table testing of a seismically isolated structure.” J. Struct. Eng. 142 (5): 04016005. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001455.
Shi, X., and S. Zhu. 2015. “Magnetic negative stiffness dampers.” Smart Mater. Struct. 24 (7): 072002. https://doi.org/10.1088/0964-1726/24/7/072002.
Shi, X., S. Zhu, J.-Y. Li, and B. F. Spencer. 2016. “Dynamic behavior of stay cables with passive negative stiffness dampers.” Smart Mater. Struct. 25 (7): 075044. https://doi.org/10.1088/0964-1726/25/7/075044.
Sun, T., Z. Lai, S. Nagarajaiah, and H.-N. Li. 2017. “Negative stiffness device for seismic protection of smart base isolated benchmark building.” Struct. Control Health Monit. 24 (11): e1968. https://doi.org/10.1002/stc.1968.
Toyooka, A., H. Motoyama, O. Kouchiyama, and Y. Iwasaki. 2015. “Development of autonomous negative stiffness damper for reducing absolute responses.” Q. Rep. RTRI 56 (4): 284–290. https://doi.org/10.2219/rtriqr.56.4_284.
Walsh, K. K. 2018. “Passive displacement-dependent damper with adjustable stiffness for seismic protection of civil infrastructure.” In Proc., 11th U.S. National Conf. on Earthquake Engineering, 25–29. Los Angeles, CA: EERI.
Walsh, K. K., E. Boso, E. P. Steinberg, J. T. Haftman, and W. N. Littell. 2018. “Variable negative stiffness device for seismic protection of building structures through apparent weakening.” J. Eng. Mech. 144 (9): 04018090. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001512.
Walsh, K. K., J. T. Haftman, and C. Marin-Artieda. 2019. Modeling and validation of a novel variable stiffness system for seismic isolation of acceleration-sensitive equipment, 438–449. Orlando, FL: Structures Congress.
Wang, M., F. Sun, and H. Jin. 2018. “Performance evaluation of existing isolated buildings with supplemental passive pseudo-negative stiffness devices.” Eng. Struct. 177 (Dec): 30–46. https://doi.org/10.1016/j.engstruct.2018.09.049.
Wu, B., P. Shi, and J. Ou. 2013. “Seismic performance of structures incorporating magnetorheological dampers with pseudo-negative stiffness.” Struct. Control Health Monit. 20 (3): 405–421. https://doi.org/10.1002/stc.504.
Xie, L., X. Ban, S. Xue, K. Ikago, J. Kang, and H. Tang. 2019. “Theoretical study on a cable-bracing inerter system for seismic mitigation.” Appl. Sci. 9 (19): 4096. https://doi.org/10.3390/app9194096.
Zhou, P., and H. Li. 2016. “Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations.” Struct. Control Health Monit. 23 (4): 764–782. https://doi.org/10.1002/stc.1809.
Zhou, Y., P. Chen, and G. Mosqueda. 2019. “Analytical and numerical investigation of quasi-zero stiffness vertical isolation system.” J. Eng. Mech. 145 (6): 04019035. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001611.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 10 • October 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Dec 30, 2019
Accepted: Mar 26, 2020
Published online: Jul 23, 2020
Published in print: Oct 1, 2020
Discussion open until: Dec 23, 2020
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.