Causal Realization of Rate-Independent Linear Damping for the Protection of Low-Frequency Structures
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
The devastating low-frequency ground motions of the 2011 Great East Japan Earthquake produced large displacements in low-frequency structures previously thought to be safe, including base-isolated structures. Rate-independent linear damping (RILD) is a promising damping model for low-frequency structures because it provides direct control over displacement. Because the control force generated by RILD is proportional to displacement (advanced in phase by radians) and independent of frequency, it performs well under both low-frequency ground motions and more common higher-frequency ground motions (relative to the structure’s fundamental natural frequency). The phase advance makes RILD noncausal, which has hindered its practical applications. This paper proposes a causal filter-based method to approximate RILD that can be easily implemented in time-domain or frequency-domain analyses. The calculated force can be tracked in real-time (due to causality) through semiactive or active control methods. The approach is applied to a base-isolated structure with supplemental control provided by a magneto-rheological (MR) damper. Both numerical simulations and shake table tests are conducted to demonstrate the performance of the proposed causal approach. The results compare well to noncausal simulations in both the achieved forces and structural responses.
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Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. 1444160 and by the Japan Society for the Promotion of Science (JSPS) under Grant-in-Aid for Scientific Research (B) No. 15H04070. The authors would also like to acknowledge Osaka Prefecture and Dr. Toshihide Kashima of the Building Research Institute of Japan for providing the Sakishima site record of the 2011 Great East Japan Earthquake.
References
Biot, M. A. (1958). “Linear thermodynamics and the mechanics of solids.” Proc., 3rd U.S. National Congress of Applied Mechanics, ASME, New York, 1–18.
Bishop, R. E. D. (1955). “The treatment of damping forces in vibration theory.” J. R. Aeronaut. Soc., 59(539), 738–742.
Carlson, J. D., and Jolly, M. R. (2000). “MR fluid, foam, and elastomer devices.” Mechatronics, 10(4–5), 555–569.
Caughey, T. K., and Vijarayaroghavan, A. (1970). “Free and forced oscillations of a dynamic system with linear hysteretic damping (non-linear theory).” Int. J. Non-Linear Mech., 5(3), 533–555.
Crandall, S. H. (1963). “Dynamic response of systems with structural damping.” Air space and instruments, McGraw-Hill, New York.
Crandall, S. H. (1991). “The hysteretic damping model in vibration theory.” J. Mech. Eng. Sci. Proc. Inst. Mech. Eng., 205(1), 23–28.
Ikago, K., and Inoue, N. (2014). “Behavior of rate-independent linear damping incorporated into long-period structures subjected to strong ground motions.” Proc., 6th World Conf. on Structural Control and Monitoring, Barcelona, Spain.
Inaudi, J. A., and Kelly, J. M. (1995). “Linear hysteretic damping and the Hilbert transform.” J. Eng. Mech., 0626–0632.
Inaudi, J. A., and Makris, N. (1996). “Time domain analysis of linear hysteretic damping.” Earthquake Eng. Struct. Dyn., 25(6), 529–545.
Lancaster, P. (1960). “Free vibration and hysteretic damping.” J. R. Aeronaut. Soc., 64(592), 229.
Makris, N. (1997a). “Rigidity-plasticity-viscosity: Can electrorheological dampers protect base-isolated structures from near source ground motions?” Earthquake Eng. Struct. Dyn., 26(5), 571–591.
Makris, N. (1997b). “The causal hysteretic element.” J. Eng. Mech., 1209–1214.
Makris, N., and Chang, S. P. (2000). “Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures.” Earthquake Eng. Struct. Dyn., 29(1), 85–107.
Mimura, N., Yasuhara, K., Kawagoe, S., Yokoki, H., and Kazama, S. (2011). “Damage from the Great East Japan Earthquake and Tsunami: A quick report.” Mitigation Adaptation Strategies Global Change, 16(7), 803–818.
Muscolino, G., Palmeri, A., and Ricciardelli, F. (2005). “Time-domain response of linear hysteretic systems to deterministic and random excitations.” Earthquake Eng. Struct. Dyn., 34(9), 1129–1147.
Nashif, T. J., Jones, I. G., and Henderson, J. P. (1988). Vibration damping, Wiley, New York.
Ohtori, Y., and Christenson, R. E., Spencer, B. F. Jr., and Dyke, S. J. (2004). “Benchmark control problems for seismically excited nonlinear buildings.” J. Eng. Mech., 366–385.
Reid, T. (1956). “Free vibration and hysteretic damping.” J. R. Aeronaut. Soc., 60(544), 283.
Spanos, P. D., and Tsavachidis, S. (2001). “Deterministic and stochastic analyses of a nonlinear system with a Biot visco-elastic element.” Earthquake Eng. Struct. Dyn., 30(4), 595–612.
Takewaki, I., Murakami, S., Fujita, K., Yoshitomi, S., and Tsuji, M. (2011). “The 2011 off the Pacific coast of Tohoku earthquake and response of high-rise buildings under long-period ground motions.” Soil Dyn. Earthquake Eng., 31(11), 1511–1528.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 11, 2016
Accepted: Jan 4, 2017
Published online: Apr 17, 2017
Published in print: Sep 1, 2017
Discussion open until: Sep 17, 2017
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