Feasibility Analysis on the Attenuation of Strong Ground Motions Using Finite Periodic Lattices of Mass-in-Mass Barriers
Publication: Journal of Engineering Mechanics
Volume 142, Issue 9
Abstract
This study assesses the implementation of locally resonant metamaterials in seismic isolation applications by investigating their potential feasibility in the [0.5, 5.0] Hz frequency band. To this end, via adoption of both Bloch’s theory and classical vibration analysis, the one-dimensional mass-in-mass lattice is analyzed in three overlapping subbands and corresponding relations for the structural parameters are derived. Accordingly, a basic unit cell is proposed that incorporates a core of dense material that is suspended in a thin shell composed of a lightweight material using distributed elastomeric tendons. Initial numerical simulations on finite-dimensional lattices reveal significant potential in the proposed solution and encourage further investigation, particularly to the two-dimensional case.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Prof. Chatzi would like to gratefully acknowledge the support provided by the Albert Lück Foundation for completion of this project.
References
Anderson, J. G. (2003). “Strong-motion seismology.” International handbook of earthquake and engineering seismology, W. H. K. Lee, H. Kanamori, P. C. Jennings, and C. Kisslinger, eds., Academic Press, San Diego, CA, 937–965.
Bao, J., Shi, Z., and Xiang, H. (2012). “Dynamic responses of a structure with periodic foundations.” J. Eng. Mech., 761–769.
Bolt, B. A. (2001). “The nature of earthquake ground motion.” The seismic design handbook, F. Naeim, ed., Springer, New York, 1–45.
Cheng, Z., and Shi, Z. (2014). “Vibration attenuation properties of periodic rubber concrete panels.” Constr. Build. Mater., 50, 257–265.
Cheng, Z., Shi, Z., Mo, Y. L., and Xiang, H. (2013a). “Locally resonant periodic structures with low-frequency band gaps.” J. Appl. Phys., 114(3), 033532.
Cheng, Z. B., et al. (2013b). “3D periodic foundation-based structural vibration isolation.” Proceedings of the World Congress on Engineering 2013 Vol III, WCE 2013, London, U.K., 1797–1802.
Clough, R. W., and Penzien, J. (2003). Dynamics of structures, 3rd Ed., Computers & Structures, Berkeley, CA.
Datta, T. K. (2010). Seismic analysis of structures, Wiley, Chichester, U.K.
Finocchio, G., et al. (2014). “Seismic metamaterials based on isochronous mechanical oscillators.” Appl. Phys. Lett., 104(19), 191903.
Gonella, S., To, A. C., and Liu, W. K. (2009). “Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting.” J. Mech. Phys. Solids, 57(3), 621–633.
Hirsekorn, M., Delsanto, P. P., Batra, N. K., and Matic, P. (2004). “Modelling and simulation of acoustic wave propagation in locally resonant sonic materials.” Ultrasonics, 42(1–9), 231–235.
Huang, H., Sun, C., and Huang, G. (2009). “On the negative effective mass density in acoustic metamaterials.” Int. J. Eng. Sci., 47(4), 610–617.
Huang, J., and Shi, Z. (2013a). “Application of periodic theory to rows of piles for horizontal vibration attenuation.” Int. J. Geomech., 132–142.
Huang, J., and Shi, Z. (2013b). “Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves.” J. Sound Vib., 332(19), 4423–4439.
Hussein, M. I., and Frazier, M. J. (2013). “Metadamping: An emergent phenomenon in dissipative metamaterials.” J. Sound Vib., 332(20), 4767–4774.
Hussein, M. I., Leamy, M. J., and Ruzzene, M. (2014). “Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook.” Appl. Mech. Rev., 66(4), 040802.
Jensen, J. (2003). “Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures.” J. Sound Vib., 266(5), 1053–1078.
Kelly, J. M. (1990). “Base isolation: Linear theory and design.” Earthquake Spectra, 6(2), 223–244.
Kim, S.-H., and Das, M. P. (2012). “Seismic wavenumber of metamaterials.” Mod. Phys. Lett. B, 26(17), 1250105.
Krödel, S., Thomé, N., and Daraio, C. (2015). “Wide band-gap seismic metastructures.” Extreme Mech. Lett., 4, 111–117.
Kushwaha, M. S., Halevi, P., Dobrzynski, L., and Djafari-Rouhani, B. (1993). “Acoustic band structure of periodic elastic composites.” Phys. Rev. Lett., 71(13), 2022–2025.
Lazarov, B., and Jensen, J. (2007). “Low-frequency band gaps in chains with attached non-linear oscillators.” Int. J. Non-Linear Mech., 42(10), 1186–1193.
Liu, Z., et al. (2000). “Locally resonant sonic materials.” Science, 289(5485), 1734–1736.
Liu, Z., Chan, C., and Sheng, P. (2005). “Analytic model of phononic crystals with local resonances.” Phys. Rev. B, 71(1), 014103.
Lu, M.-H., Feng, L., and Chen, Y.-F. (2009). “Phononic crystals and acoustic metamaterials.” Mater. Today, 12(12), 34–42.
Mao, L. J., and Li, A. Q. (2005). “The simplified models and their precision for analysis of multi-story sliding isolated structures.” J. Build. Struct., 26(2), 117–123.
Mitchell, S. J., Pandolfi, A., and Ortiz, M. (2014). “Metaconcrete: Designed aggregates to enhance dynamic performance.” J. Mech. Phys. Solids, 65(1), 69–81.
Ordonez, D., Foti, D., and Bozzo, L. (2003). “Comparative study of the inelastic response of base isolated buildings.” Earthquake Eng. Struct. Dyn., 32(1), 151–164.
Providakis, C. (2009). “Effect of supplemental damping on LRB and FPS seismic isolators under near-fault ground motions.” Soil Dyn. Earthquake Eng., 29(1), 80–90.
Sheng, P., Mei, J., Liu, Z., and Wen, W. (2007). “Dynamic mass density and acoustic metamaterials.” Phys. B Condens. Matter, 394(2), 256–261.
Sheng, P., Zhang, X., Liu, Z., and Chan, C. (2003). “Locally resonant sonic materials.” Phys. B Condens. Matter, 338(1–4), 201–205.
Shi, Z., Cheng, Z., and Xiang, H. (2014). “Seismic isolation foundations with effective attenuation zones.” Soil Dyn. Earthquake Eng., 57, 143–151.
Sigalas, M. and Economou, E. (1992). “Elastic and acoustic wave band structure.” J. Sound Vib., 158(2), 377–382.
Vasseur, J. O., Djafari-Rouhani, B., Dobrzynski, L., Kushwaha, M. S., and Halevi, P. (1994). “Complete acoustic band gaps in periodic fibre reinforced composite materials: The carbon/epoxy composite and some metallic systems.” J. Phys. Condens. Matter, 6(42), 8759–8770.
Wang, W.-C., Wu, L.-Y., Chen, L.-W., and Liu, C.-M. (2010). “Acoustic energy harvesting by piezoelectric curved beams in the cavity of a sonic crystal.” Smart Mater. Struct., 19(4), 045016.
Woods, R. D., Barnett, N. E., and Sagesser, R. (1974). “Holography—A new tool for soil dynamics.” J. Geotech. Geoenviron. Eng., 100(11), 17.
Wu, L.-Y., Chen, L.-W., and Liu, C.-M. (2009). “Acoustic energy harvesting using resonant cavity of a sonic crystal.” Appl. Phys. Lett., 95(1), 013506.
Xiang, H. J., Shi, Z. F., Wang, S. J., and Mo, Y. L. (2012). “Periodic materials-based vibration attenuation in layered foundations: Experimental validation.” Smart Mater. Struct., 21(11), 112003.
Yan, Y., et al. (2014). “Seismic isolation of two dimensional periodic foundations.” J. Appl. Phys., 116(4), 044908.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 21, 2015
Accepted: Mar 25, 2016
Published online: May 11, 2016
Published in print: Sep 1, 2016
Discussion open until: Oct 11, 2016
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.