Abstract
A novel nonlinear isolation system designed for buildings is proposed to isolate vibrations in the vertical direction. The system is characterized by quasi-zero stiffness (QZS) obtained by combining linear springs in parallel with disk springs having nonlinear stiffness, including a region with negative stiffness. Static analysis was first applied to establish the force-displacement relation of the bearings and then determine the dynamic equations of motion. Two approximate analytical methods, the average method (AM) and harmonic balance method (HBM), were applied to solve this nonlinear vibration problem, and their suitability was examined. Based on the theoretical response, the transmissibility function was defined to gain insight into the system’s dynamic characteristics and evaluate the isolation properties. The resulting curves show that the QZS system can be effective for vertical isolation, with results dependent on external input magnitude and the damping level. Larger-amplitude excitation and higher damping level tend to increase the isolation starting frequency above which the transmissibility reduces the vibration of the superstructure. Finally, the nonlinear transmissibility curves were compared with equivalent linear curves, and a numerical comparison between a traditional building and a QZS vertically isolated building under seismic excitations was conducted. The comparison revealed significant advantages to adopting the QZS system in vertical isolation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge the financial support from National Natural Science Foundation of China (Grant No. 51322803) and China Scholarship Council (CSC).
References
Alabuzhev, P., and E. I. Rivin. 1989. Vibration protection and measuring systems with quasi-zero stiffness. Boca Raton, FL: CRC Press.
Amabili, M., F. Pellicano, and M. Paidoussis. 1998. “Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid.” J. Fluids Struct. 12 (7): 883–918. https://doi.org/10.1006/jfls.1998.0173.
Ancheta, T. D., R. B. Darragh, J. P. Stewart, E. Seyhan, W. J. Silva, B. S. Chiou, and T. Kishida. 2013. “NGA-West2 database.” Pacific Earthquake Engineering Research (PEER) Center. 2018. Accessed September 30, 2017. https://ngawest2.berkeley.edu.
Araki, Y., T. Asai, and T. Masui. 2009. “Vertical vibration isolator having piecewise-constant restoring force.” Earthquake Eng. Struct. Dyn. 38 (13): 1505–1523. https://doi.org/10.1002/eqe.915.
Carrella, A., M. Brennan, and T. Waters. 2007. “Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic.” J. Sound Vib. 301 (3–5): 678–689. https://doi.org/10.1016/j.jsv.2006.10.011.
Christopoulos, C., A. Filiatrault, and V. V. Bertero. 2006. Principles of passive supplemental damping and seismic isolation. Pavia, Italy: IUSS Press.
Code of China. 2010. Code for seismic design of buildings. GB 50011-2010. Beijing: China Architecture and Building Press.
Cui, G., X. Tao, and X. Chen. 2008. “Studies on environmental vibration induced by urban rail transit.” Earthquake Eng. Eng. Vib.-Chinese Edition 28 (1): 38.
Fujita, T. 1985. “Earthquake isolation technology for industrial facilities—Research, development and applications in Japan.” Bull. New Zealand Nat. Soc. Earthquake Eng. 18 (3): 224–249.
Gilmore, R. J., and M. B. Steer. 1991. “Nonlinear circuit analysis using the method of harmonic balance method-a review of the art. Part I. Introductory concepts.” Int. J. RF Microwave Comput.-Aided Eng. 1 (1): 22–37. https://doi.org/10.1002/mmce.4570010104.
Guzman Pujols, J. C., and K. L. Ryan. 2017. “Slab vibration and horizontal-vertical coupling in the seismic response of low-rise irregular base-isolated and conventional buildings.” J. Earthquake Eng. 1–36. https://doi.org/10.1080/13632469.2017.1387197.
Guzman Pujols, J. C., and K. L. Ryan. 2018. “Computational simulation of slab vibration and horizontal-vertical coupling in a full-scale test bed subjected to 3D shaking at E-defense.” Earthquake Eng. Struct. Dyn. 47 (2): 438–459. https://doi.org/10.1002/eqe.2973.
Kovacic, I., M. J. Brennan, and T. P. Waters. 2008. “A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic.” J. Sound Vib. 315 (3): 700–711. https://doi.org/10.1016/j.jsv.2007.12.019.
Li, W., Y. G. Tang, L. Q. Liu, Y. Li, and B. Wang. 2017. “Internal resonances for heave, roll and pitch modes of a spar platform considering wave and vortex-induced loads in the main roll resonance.” China Ocean Eng. 31 (4): 408–417. https://doi.org/10.1007/s13344-017-0047-9.
Li, Y. M., and W. X. Shi. 2013. “Experimental study on mechanical property of a composite isolation bearing.” Build. Struct. 43 (13): 1–4.
Liu, C., X. Jing, S. Daley, and F. Li. 2015. “Recent advances in micro-vibration isolation.” Mech. Syst. Signal Process. 56: 55–80. https://doi.org/10.1016/j.ymssp.2014.10.007.
Lu, L. Y., P. R. Chen, and K. W. Pong. 2016. “Theory and experiment of an inertia-type vertical isolation system for seismic protection of equipment.” J. Sound Vib. 366: 44–61. https://doi.org/10.1016/j.jsv.2015.12.009.
Meng, L., J. Sun, and W. Wu. 2015. “Theoretical design and characteristics analysis of a quasi-zero stiffness isolator using a disk spring as negative stiffness element.” Shock Vib. 2015: 813763. https://doi.org/10.1155/2015/813763.
Nayfeh, A. H. 2011. Introduction to perturbation techniques. New York: Wiley.
Nicolosi, V., M. D’Apuzzo, and E. Bogazzi. 2012. “A unified approach for the prediction of vibration induced by underground metro.” Procedia-Sociol Behav. Sci. 53: 62–71. https://doi.org/10.1016/j.sbspro.2012.09.860.
Papazoglou, A., and A. Elnashai. 1996. “Analytical and field evidence of the damping effect of vertical earthquake ground motion.” Earthquake Eng. Struct. Dyn. 25 (10): 1109–1137. https://doi.org/10.1002/(SICI)1096-9845(199610)25:10%3C1109::AID-EQE604%3E3.0.CO;2-0.
Pasala, D., A. Sarlis, S. Nagarajaiah, A. Reinhorn, M. Constantinou, and D. Tylor. 2012. “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.
Salazar, A. R., and A. Haldar. 2000. “Structural response considering the vertical component of earthquakes.” Comput. Struct. 74 (2): 131–145. https://doi.org/10.1016/S0045-7949(99)00031-0.
Shen, W., and Y. G. Tang. 2011. “Stochastic analysis of nonlinear coupled heave-pitch motion for truss spar platform.” J. Mar. Sci. Appl. 10 (4): 471–477. https://doi.org/10.1007/s11804-011-1093-y.
Suhara, J., T. Tamura, Y. Okada, and K. Umeki. 2002. “Development of three dimensional seismic isolation device with laminated rubber bearing and rolling seal type air spring.” In Proc., ASME 2002 Pressure Vessels and Piping Conf., 43–48. New York: ASME.
Tsuji, Y., T. Sasaki, T. P. Waters, K. Fujito, and D. Wang. 2014. “A nonlinear vibration isolator based on a post-buckled inverted L-shaped beam.” In Proc., 6th World Conf. on Structural Control and Monitoring (WCSCM). Barcelona, Spain: International Association for Structural Control and Monitoring.
Wagg, D., and S. Neild. 2009. Nonlinear vibration with control. New York: Springer.
Worden, K., and G. R. Tomlinson. 2000. Nonlinearity in structural dynamics: Detection, identification and modelling. Boca Raton, FL: CRC Press.
Yonekawa, Y., S. Maeda, K. Kanada, and Y. Takahashi. 1999. “Whole-body vibration perception thresholds of recumbent subjects.” Ind. Health 37 (4): 398–403. https://doi.org/10.2486/indhealth.37.398.
Zhao, J. R., Y. G. Tang, and W. J. Shen. 2010. “A study on the combination resonance response of a classic spar platform.” J. Vib. Control 16 (14): 2083–2107. https://doi.org/10.1177/1077546309349393.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 6 • June 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Feb 16, 2018
Accepted: Nov 8, 2018
Published online: Mar 25, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 25, 2019
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.