Modified Generalized Maxwell Model for Hysteresis Behavior of Elastomeric Dampers
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 146, Issue 8
Abstract
A constitutive model is presented for the hysteretic behavior of elastomeric material, called the modified generalized Maxwell model (MGMM). A new force-displacement relationship that describes the well known generalized Maxwell model (GMM) is also proposed in this study and forms the basis for the MGMM. This relationship can be used regardless of the number of Maxwell elements. The damper was first characterized using terms of the viscoelastic (VE) material, determining its shear storage modulus and loss factor for a range of cyclic tests. This led not only to an understanding of how the main mechanical properties of the damper change when the strain amplitude, frequency, and temperature change but also to a more detailed understanding of how the hysteresis shape of the material changes along the alteration of these parameters. The final model was calibrated using test data obtained from sweep amplitude tests over a range of frequencies and ambient temperatures and was able to accurately predict the dynamic performance of the dampers.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
We thank Alan Muhr and Hamid Ahmadi of the Tun Abdul Razak Research Centre for their support of this work and the donation of test devices and the UK Engineering and Physical Sciences Research Council for their financial support of the first author.
References
Aiken, I. 1997. “An analytical hysteresis model for elastomeric seismic isolation bearings.” Earthquake Eng. Struct. Dyn. 26 (2): 215–231. https://doi.org/10.1002/(SICI)1096-9845(199702)26:2%3C215::AIDEQE640%3E 3.0.CO;2-9.
Bland, D. 1960. The theory of linear viscoelasticity. Oxford: Pergamon Press.
Constantinou, M. C., T. T. Soong, and G. F. Dargush. 1998. Passive energy dissipation systems for structural design and retrofit. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research.
Constantinou, M. C., and I. G. Tadjbakhsh. 1985. “Hysteretic dampers in base isolation: Random approach.” J. Struct. Eng. 111 (4): 705–721. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(705).
Dahl, P. R. 1968. A solid friction model. El Segundo, CA: Aerospace Corporation.
Dorka, U., and J. Garcia. 2005. Seismic qualification of passive mitigation devices. Cooperative advancements in seismic and dynamic experiments. Lisboa, Portugal: Laboratorio Nacional de Engenharia Civil.
Fan, C. P. 1998. “Seismic analysis, behavior, and retrofit of non-ductile reinforced concrete frame buildings with viscoelastic dampers.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Lehigh Univ.
Ferry, J. D. 1980. Viscoelastic properties of polymers. New York: Wiley.
Hepburn, C., and R. Reynolds. 1979. Elastomers: Criteria for engineering design. London: Applied Science Publishers.
Hwang, J., and J. Wang. 1998. “Seismic response prediction of HDR bearings using fractional derivative Maxwell model.” Eng. Struct. 20 (9): 849–856. https://doi.org/10.1016/S0141-0296(98)80005-9.
Jrad, H., J. L. Dion, F. Renaud, I. Tawfiq, and M. Haddar. 2013. “Experimental characterization, modeling and parametric identification of the non linear dynamic behavior of viscoelastic components.” Eur. J. Mech. A/Solids 42 (Nov): 176–187. https://doi.org/10.1016/j.euromechsol.2013.05.004.
Jrad, H., J. L. Dion, F. Renaud, I. Tawfiq, and M. Haddar. 2017. “Experimental and numerical investigation of energy dissipation in elastomeric rotational joint under harmonic loading.” Mech. Time-Depend. Mater. 21 (2): 177–198. https://doi.org/10.1007/s11043-016-9325-9.
Karavasilis, T. L., T. Blakeborough, and M. S. Williams. 2011. “Development of nonlinear analytical model and seismic analyses of a steel frame with self-centering devices and viscoelastic dampers.” Comput. Struct. 89 (11): 1232–1240. https://doi.org/10.1016/j.compstruc.2010.08.013.
Karavasilis, T. L., R. Sause, and J. M. Ricles. 2012. “Seismic design and evaluation of steel moment-resisting frames with compressed elastomer dampers.” Earthquake Eng. Struct. Dyn. 41 (3): 411–429. https://doi.org/10.1002/eqe.1136.
Kästner, M., M. Obst, J. Brummund, K. Thielsch, and V. Ulbricht. 2012. “Inelastic material behavior of polymers—Experimental characterization, formulation and implementation of a material model.” Mech. Mater. 52 (Sep): 40–57. https://doi.org/10.1016/j.mechmat.2012.04.011.
Kit Miyamoto, M., and L. M. Determan. n.d. “Structural applications of Taylor fluid viscous dampers.” Accessed October 4, 2017. http://www.taylordevices.com/custom/pdf/tech-papers/70-SeismicRehabilitationofHCS.pdf.
Koh, C. G., and J. M. Kelly. 1990. “Application of fractional derivatives to seismic analysis of base-isolated models.” Earthquake Eng. Struct. Dyn. 19 (2): 229–241. https://doi.org/10.1002/eqe.4290190207.
Lai, M., P. Lu, D. Lunsford, K. Kasai, and K. Chang. 1996. “Viscoelastic damper: A damper with linear or nonlinear material.” In Proc., 11th World Conf. on Earthquake Engineering. Acapulco, Mexico: Pergamon.
Lee, K. S. 2003. “Seismic behavior of structures with dampers made from ultra high damping natural rubber.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Lehigh Univ.
Mahmoodi, P., L. Robertson, M. Yontar, C. Moy, and L. Feld. 1987. “Performance of viscoelastic dampers in World Trade Center towers.” In Dynamics of structures, 632–644. Reston, VA: ASCE.
Makris, N., and M. Constantinou. 1991. “Fractional-derivative Maxwell model for viscous dampers.” J. Struct. Eng. 117 (9): 2708–2724. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:9(2708).
McCrum, N. G., C. Buckley, and C. B. Bucknall. 1997. Principles of polymer engineering. Oxford: Oxford University Press.
Nashif, A. D., D. I. Jones, and J. P. Henderson. 1985. Vibration damping. New York: Wiley.
Pant, D., M. Montgomery, C. Christopoulos, and D. Poon. 2017. “Viscoelastic coupling dampers for the enhanced seismic resilience of a megatall building.” In Vol. 1318 of Proc., 16th World Conf. on Earthquake Engineering, 16WCEE 2017. Santiago, Chile: Chilean Association on Seismology and Earthquake Engineering.
Papoulia, K. D., and J. M. Kelly. 1994. Material characterization of elastomers used in earthquake base isolation. Berkeley, CA: Univ. of California.
Petrone, F., M. Lacagnina, and M. Scionti. 2004. “Dynamic characterization of elastomers and identification with rheological models.” J. Sound Vib. 271 (1): 339–363. https://doi.org/10.1016/j.jsv.2003.02.001.
Prestandard. 2000. Commentary for the seismic rehabilitation of buildings (FEMA356). Washington, DC: Federal Emergency Management Agency.
Sause, R., K.-S. Lee, and J. Ricles. 2007. “Rate-independent and rate-dependent models for hysteretic behavior of elastomers.” J. Eng. Mech. 133 (11): 1162–1170. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:11(1162).
Shen, K., and T. Soong. 1995. “Modeling of viscoelastic dampers for structural applications.” J. Eng. Mech. 121 (6): 694–701. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:6(694).
Shrimali, M., S. Bharti, and S. Dumne. 2015. “Seismic response analysis of coupled building involving MR damper and elastomeric base isolation.” Ain Shams Eng. J. 6 (2): 457–470. https://doi.org/10.1016/j.asej.2014.12.007.
Silwal, B., R. J. Michael, and O. E. Ozbulut. 2015. “A superelastic viscous damper for enhanced seismic performance of steel moment frames.” Eng. Struct. 105 (Dec): 152–164. https://doi.org/10.1016/j.engstruct.2015.10.005.
Soong, T. T., and G. F. Dargush. 1997. Passive energy dissipation systems in structural engineering. New York: Wiley.
Summers, P., P. Jacob, J. Marti, G. Bergamo, L. Dorfmann, G. Castellano, A. Poggianti, D. Karabalis, H. Silbe, and S. Triantafillou. 2004. “Development of new base isolation devices for application at refineries and petrochemical facilities.” In Proc., 13th World Conf. on Earthquake Engineering, 1–6. Vancouver, BC, Canada: 13 WCEE Secretariat.
Taniwangsa, W., and J. Kelly. 1996. “Studies on seismic isolation for housing in developing regions.” In Proc., 11th World Conf. on Earthquake Engineering. Acapulco, Mexico: Pergamon.
Teramoto, T., H. Kitamura, and H. Ozaki. 1996. “Practical application of high-damping rubber dampers to a slender building.” In Vol. 1801 of Proc., 11th World Conf. on Earthquake Engineering, 11 WCEE 1996. Acapulco, Mexico: Pergamon.
Torvik, P., and R. Bagley. 1984. “On the appearance of the fractional derivative in the behavior of real materials.” J. Appl. Mech. Trans. ASME. 51 (2): 294–298. https://doi.org/10.1115/1.3167615.
Vargas, R., and M. Bruneau. 2007. “Effect of supplemental viscous damping on the seismic response of structural systems with metallic dampers.” J. Struct. Eng. 133 (10): 1434–1444. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:10(1434).
Yu, Y., Y. Li, J. Li, and X. Gu. 2016. “A hysteresis model for dynamic behaviour of magnetorheological elastomer base isolator.” Smart Mater. Struct. 25 (5): 055029. https://doi.org/10.1088/0964-1726/25/5/055029.
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©2020 American Society of Civil Engineers.
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Received: Jun 5, 2019
Accepted: Feb 12, 2020
Published online: Jun 10, 2020
Published in print: Aug 1, 2020
Discussion open until: Nov 10, 2020
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