Partially Embedded Gradient Metabarrier: Broadband Shielding from Seismic Rayleigh Waves at Ultralow Frequencies
Publication: Journal of Engineering Mechanics
Volume 146, Issue 5
Abstract
A partially embedded gradient metabarrier (PEGM) for seismic Rayleigh waves was designed and studied using the finite-element method (FEM). Investigations on the partially embedded periodic metabarrier (PEPM) were carried out first, and relations between band gaps (BGs) and some sensitive parameters were examined in detail. A PEGM and piecewise PEGM were then designed and discussed based on these investigations. It was found that BGs at ultralow frequencies can be obtained by the PEPM and effectively tuned by the geometrical parameters, especially the embedded depth. The PEGM broadens the frequency attenuation zone significantly, and the piecewise PEGM further extends the zone to cover the main frequency range of seismic waves from 1 to 20 Hz. Surface wave with tens of meters wavelength can be successfully controlled by the designed meter-scaled metabarrier. Simulations of the transmission spectra of El Centro and Taft waves showed that the piecewise PEGM exhibits high efficiency of earthquake shielding.
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Data Availability Statement
All data used during the study are available from the corresponding author by request.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (11772040).
References
Achaoui, Y., T. Antonakakis, S. Brule, R. V. Craster, S. Enoch, and S. Guenneau. 2017. “Clamped seismic metamaterials: Ultra-low broad frequency stop-bands.” New J. Phys. 19 (6): 063022. https://doi.org/10.1088/1367-2630/aa6e21.
Achenbach, J. D. 1973. Wave propagation in elastic solids, edited by H. A. Lauwerier and W. T. Koiter, 192–193. Amsterdam, Netherlands: Northholand.
Assouar, B. M., and M. Oudich. 2011. “Dispersion curves of surface acoustic waves in a two-dimensional phononic crystal.” Appl. Phys. Lett. 99 (12): 123505. https://doi.org/10.1063/1.3626853.
Banerjee, B. 2011. An introduction to metamaterials and waves in composites. Boca Raton, FL: CRC Press.
Bilham, R. 2010. “Lessons from the Haiti earthquake.” Nature 463 (7283): 878. https://doi.org/10.1038/463878a.
Brûlé, S., E. H. Javelaud, S. Enoch, and S. Guenneau. 2014. “Experiments on seismic metamaterials: Molding surface waves.” Phys. Rev. Lett. 112 (13): 133901. https://doi.org/10.1103/PhysRevLett.112.133901.
Cheng, Z., W. Lin, and Z. Shi. 2018. “Wave dispersion analysis of multi-story frame building structures using the periodic structure theory.” Soil Dyn. Earthquake Eng. 106 (Mar): 215–230. https://doi.org/10.1016/j.soildyn.2017.12.024.
Colombi, A., D. Colquitt, P. Roux, S. Guenneau, and R. V. Craster. 2016a. “A seismic metamaterial: The resonant metawedge.” Sci. Rep. 6 (1): 27717. https://doi.org/10.1038/srep27717.
Colombi, A., P. Roux, S. Guenneau, P. Gueguen, and R. V. Craster. 2016b. “Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances.” Sci. Rep. 6 (1): 19238. https://doi.org/10.1038/srep19238.
Dertimanis, V. K., I. A. Antoniadis, and E. N. Chatzi. 2016. “Feasibility analysis on the attenuation of strong ground motions using finite periodic lattices of mass-in-mass barriers.” J. Eng. Mech. 142 (9): 04016060. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001120.
Ding, Y., Z. Liu, C. Qiu, and J. Shi. 2007. “Metamaterial with simultaneously negative bulk modulus and mass density.” Phys. Rev. Lett. 99 (9): 093904. https://doi.org/10.1103/PhysRevLett.99.093904.
Du, Q., Y. Zeng, G. Huang, and H. Yang. 2017. “Elastic metamaterial-based seismic shield for both Lamb and surface waves.” AIP Adv. 7 (7): 075015. https://doi.org/10.1063/1.4996716.
Du, Q., Y. Zeng, Y. Xu, H. Yang, and Z. Zeng. 2018. “H-fractal seismic metamaterial with broadband low-frequency bandgaps.” J. Phys. D: Appl. Phys. 51 (10): 105104. https://doi.org/10.1088/1361-6463/aaaac0.
Kim, S. H., and M. P. Das. 2012. “Seismic waveguide of metamaterials.” Mod. Phys. Lett. B 26 (17): 1250105. https://doi.org/10.1142/S0217984912501059.
Krödel, S., N. Thomé, and C. Daraio. 2015. “Wide band-gap seismic metastructures.” Extrem. Mech. Lett. 4 (Sep): 111–117. https://doi.org/10.1016/j.eml.2015.05.004.
Kushwaha, M. S., P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani. 1993. “Acoustic band structure of periodic elastic composites.” Phys. Rev. Lett. 71 (13): 2022. https://doi.org/10.1103/PhysRevLett.71.2022.
Liu, Z., C. T. Chan, and P. Sheng. 2005. “Analytic model of phononic crystals with local resonances.” Phys. Rev. B 71 (1): 014103. https://doi.org/10.1103/PhysRevB.71.014103.
Liu, Z., X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng. 2000. “Locally resonant sonic materials.” Science 289 (5485): 1734–1736. https://doi.org/10.1126/science.289.5485.1734.
Maleki, M., and M. I. Khodakarami. 2017. “Feasibility analysis of using MetaSoil scatterers on the attenuation of seismic amplification in a site with triangular hill due to SV-waves.” Soil Dyn. Earthquake Eng. 100 (Sep): 169–182. https://doi.org/10.1016/j.soildyn.2017.05.036.
Miniaci, M., A. Krushynska, F. Bosia, and N. M. Pugno. 2016. “Large scale mechanical metamaterials as seismic shields.” New J. Phys. 18 (8): 083041. https://doi.org/10.1088/1367-2630/18/8/083041.
Oudich, M., and A. M. Badreddine. 2012. “Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for high frequency applications.” J. Appl. Phys. 111 (1): 014504. https://doi.org/10.1063/1.3673874.
Palermo, A., S. Krödel, A. Marzani, and C. Daraio. 2016. “Engineered metabarrier as shield from seismic surface waves.” Sci. Rep. 6 (1): 39356. https://doi.org/10.1038/srep39356.
Palermo, A., S. Krödel, K. H. Matlack, R. Zaccherini, V. K. Dertimanis, E. N. Chatzi, A. Marzani, and C. Daraio. 2018a. “Hybridization of guided surface acoustic modes in unconsolidated granular media by a resonant metasurface.” Phys. Rev. Appl. 9 (5): 054026. https://doi.org/10.1103/PhysRevApplied.9.054026.
Palermo, A., M. Vitali, and A. Marzani. 2018b. “Metabarriers with multi-mass locally resonating units for broad band Rayleigh waves attenuation.” Soil Dyn. Earthquake Eng. 113 (Oct): 265–277. https://doi.org/10.1016/j.soildyn.2018.05.035.
PEER Ground Motion Database. 2018. Accessed September 25, 2018. https://ngawest2.berkeley.edu/.
Pu, X., and Z. Shi. 2017. “A novel method for identifying surface waves in periodic structures.” Soil Dyn. Earthquake Eng. 98 (Jul): 67–71. https://doi.org/10.1016/j.soildyn.2017.04.011.
Schwan, L., and C. Boutin. 2013. “Unconventional wave reflection due to resonant surface.” Wave Motion 50 (4): 852–868. https://doi.org/10.1016/j.wavemoti.2013.02.010.
Sheng, P., J. Mei, Z. Liu, and W. Wen. 2007. “Dynamic mass density and acoustic metamaterials.” Phys. B: Cond. Matter. 394 (2): 256–261. https://doi.org/10.1016/j.physb.2006.12.046.
Shi, Z., Z. Cheng, and C. Xiong. 2010. “A new seismic isolation method by using a periodic foundation.” In Earth and space 2010: Engineering, science, construction, and operations in challenging environments, 2586–2594. Reston, VA: ASCE. https://doi.org/10.1061/41096(366)242.
Wagner, P. R., V. K. Dertimanis, I. A. Antoniadis, and E. N. Chatzi. 2016. “On the feasibility of structural metamaterials for seismic-induced vibration mitigation.” Int. J. Earthquake Impact Eng. 1 (1–2): 20–56. https://doi.org/10.1504/IJEIE.2016.080032.
Wagner, P. R., V. K. Dertimanis, E. N. Chatzi, and J. L. Beck. 2017. “Robust-to-uncertainties optimal design of seismic metamaterials.” J. Eng. Mech. 144 (3): 04017181. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001404.
Zeng, Y., Y. Xu, K. Deng, Z. Zeng, H. Yang, M. Muzamil, and Q. Du. 2018. “Low-frequency broadband seismic metamaterial using I-shaped pillars in a half-space.” J. Appl. Phys. 123 (21): 214901. https://doi.org/10.1063/1.5021299.
Zhou, X. Z., Y. S. Wang, and C. Zhang. 2009. “Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals.” J. Appl. Phys. 106 (1): 014903. https://doi.org/10.1063/1.3159644.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jan 3, 2019
Accepted: Oct 25, 2019
Published online: Feb 28, 2020
Published in print: May 1, 2020
Discussion open until: Jul 28, 2020
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