Bandgap Characteristics and Seismic Applications of Inerter-in-Lattice Metamaterials
Publication: Journal of Engineering Mechanics
Volume 145, Issue 9
Abstract
Longitudinal elastic wave propagation characteristics of a proposed inerter-in-lattice metamaterial (ILM) were investigated. Its local resonance emerges from the additional degree of freedom induced by a series combination of a spring element and an inerter in the lattice. The presence of inerters provides a means to reduce expenses in terms of the associated mass compared with locally resonant metamaterials (LRMs). Parametric studies of the number of cells, mass ratios, and damping ratios of finite ILM lattices were conducted. Those parameters affect not only widths and depths of attenuation zones but also resonant responses in nonattenuation zones, which is important for seismic applications. Wave propagations in finite lattices were investigated in perspective of energy, and it was found that both quantities of input energy and energy spatial distributions are different when excitation frequencies fall in passbands and stopbands, respectively. A conceptual configuration of the unit cell for ILMs applied as a seismic barrier was proposed. Numerical simulations of the barrier under excitations of three seismic records revealed its feasibility for the attenuation of ground motions.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support by National Natural Science Foundation of China (No. 51778488) is greatly acknowledged.
References
Acar, G., and C. Yilmaz. 2013. “Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures.” J. Sound Vib. 332 (24): 6389–6404. https://doi.org/10.1016/j.jsv.2013.06.022.
Achaoui, Y., B. Ungureanu, S. Enoch, S. Brûlé, and S. Guenneau. 2015. “Seismic waves damping with arrays of inertial resonators.” Extreme Mech. Lett. 8 (Sep): 30–37. https://doi.org/10.1016/j.eml.2016.02.004.
Anoyatis, G., R. D. Laora, A. Mandolini, and G. Mylonakis. 2013. “Kinematic response of single piles for different boundary conditions: Analytical solutions and normalization schemes.” Soil Dyn. Earthquake Eng. 44 (1): 183–195. https://doi.org/10.1016/j.soildyn.2012.09.011.
Antoniadis, I., D. Chronopoulos, V. Spitas, and D. Koulocheris. 2015. “Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element.” J. Sound Vib. 346 (Jun): 37–52. https://doi.org/10.1016/j.jsv.2015.02.028.
Aravantinos-Zafiris, N., and M. M. Sigalas. 2015. “Large scale phononic metamaterials for seismic isolation.” J. Appl. Phys. 118 (6): 064901. https://doi.org/10.1063/1.4928405.
Bao, J., Z. Shi, and H. Xiang. 2012. “Dynamic responses of a structure with periodic foundations.” J. Eng. Mech. 138 (7): 761–769. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000383.
Cheng, Z. B., and Z. F. Shi. 2013. “Novel composite periodic structures with attenuation zones.” Eng. Struct. 56 (Nov): 1271–1282. https://doi.org/10.1016/j.engstruct.2013.07.003.
Cheng, Z. B., and Z. F. Shi. 2014. “Multi-mass-spring model and energy transmission of one-dimensional periodic structures.” IEE Trans. Ultrason. Ferroelectr. Freq. Control 61 (5): 739. https://doi.org/10.1109/TUFFC.2014.2966.
Cheng, Z. B., and Z. F. Shi. 2018. “Composite periodic foundation and its application for seismic isolation.” Earthquake Eng. Struct. Dyn. 47 (4): 925–944. https://doi.org/10.1002/eqe.2999.
Colombi, A., D. Colquitt, P. Roux, S. Guenneau, and R. V. Craster. 2016. “A seismic metamaterial: The resonant metawedge.” Sci. Rep. 6: 27717. https://doi.org/10.1038/srep27717.
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.
Elford, D. P., L. Chalmers, F. V. Kusmartsev, and G. M. Swallowe. 2011. “Matryoshka locally resonant sonic crystal.” J. Acoust. Soc. Am. 130 (5): 2746–2755. https://doi.org/10.1121/1.3643818.
Finocchio, G., O. Casablanca, G. Ricciardi, U. Alibrandi, F. Garesci, M. Chiappini, and B. Azzerboni. 2014. “Seismic metamaterials based on isochronous mechanical oscillators.” Appl. Phys. Lett. 104 (19): 191903. https://doi.org/10.1063/1.4876961.
Garrido, H., O. Curadelli, and D. Ambrosini. 2013. “Improvement of tuned mass damper by using rotational inertia through tuned viscous mass damper.” Eng. Struct. 56 (6): 2149–2153. https://doi.org/10.1016/j.engstruct.2013.08.044.
Goffaux, C., J. Sanchez-Dehesa, A. L. Yeyati, P. Lambin, A. Khelif, J. O. Vasseur, and B. Djafari-Rouhani. 2002. “Evidence of Fano-like interference phenomena in locally resonant materials.” Phys. Rev. Lett. 88 (22): 225502. https://doi.org/10.1103/PhysRevLett.88.225502.
Gonzalez-Buelga, A., I. F. Lazar, J. Z. Jiang, S. A. Neild, and D. J. Inman. 2017. “Assessing the effect of nonlinearities on the performance of a tuned inerter damper.” Struct. Control Health Monit. 24 (3): e1879. https://doi.org/10.1002/stc.1879.
Huang, H. H., and C. T. Sun. 2009. “Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density.” New J. Phys. 11 (1): 013003. https://doi.org/10.1088/1367-2630/11/1/013003.
Huang, J., and Z. Shi. 2013. “Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves.” J. Sound Vib. 332 (19): 4423–4439. https://doi.org/10.1016/j.jsv.2013.03.028.
Huang, J., Z. Shi, W. Huang, X. Chen, and Z. Zhang. 2017. “A periodic foundation with rotational oscillators for extremely low-frequency seismic isolation: Analysis and experimental verification.” Smart Mater. Struct. 26 (3): 035061. https://doi.org/10.1088/1361-665X/aa5dd1.
Hussein, M. I., and M. J. Frazier. 2013. “Metadamping: An emergent phenomenon in dissipative metamaterials.” J. Sound Vib. 332 (20): 4767–4774. https://doi.org/10.1016/j.jsv.2013.04.041.
Hussein, M. I., M. J. Leamy, and M. Ruzzene. 2014. “Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook.” Appl. Mech. Rev. 66 (4): 040802. https://doi.org/10.1115/1.4026911.
Ikago, K., K. Saito, and N. Inoue. 2012. “Seismic control of single-degree-of-freedom structure using tuned viscous mass damper.” Earthquake Eng. Struct. Dyn. 41 (3): 453–474. https://doi.org/10.1002/eqe.1138.
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.” Extreme Mech. Lett. 4 (Sep): 111–117. https://doi.org/10.1016/j.eml.2015.05.004.
Kulkarni, P. P., and J. M. Manimala. 2016. “Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials.” J. Appl. Phys. 119 (24): 245101. https://doi.org/10.1063/1.4954074.
La Salandra, V., M. Wenzel, O. S. Bursi, G. Carta, and A. B. Movchan. 2017. “Conception of a 3D metamaterial-based foundation for static and seismic protection of fuel storage tanks.” Front. Mater. 4: 30. https://doi.org/10.3389/fmats.2017.00030.
Liu, Y., J. Yi, Z. Li, X. Su, W. Li, and M. Negahban. 2017. “Dissipative elastic metamaterial with a low-frequency passband.” AIP Adv. 7 (6): 065215. https://doi.org/10.1063/1.4991034https://doi.org/10.1063/1.4991034.
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.
Makris, N., and G. Kampas. 2016. “Seismic protection of structures with supplemental rotational inertia.” J. Eng. Mech. 142 (11): 04016089. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001152.
Manimala, J. M., and C. T. Sun. 2014. “Microstructural design studies for locally dissipative acoustic metamaterials.” J. Appl. Phys. 115 (2): 023518. https://doi.org/10.1063/1.4861632.
Palermo, A., S. Krödel, A. Marzani, and C. Daraio. 2016. “Engineered metabarrier as shield from seismic surface waves.” Sci. Rep. 6: 39356. https://doi.org/10.1038/srep39356.
Persson, P., K. Persson, and G. Sandberg. 2016. “Numerical study of reduction in ground vibrations by using barriers.” Eng. Struct. 115 (May): 18–27. https://doi.org/10.1016/j.engstruct.2016.02.025.
Santana, A., J. J. Aznárez, L. A. Padrón, and O. Maeso. 2018. “A criterion to assess the relevance of structural flexibility on the seismic response of large buried structures.” Soil Dyn. Earthquake Eng. 106 (Mar): 243–253. https://doi.org/10.1016/j.soildyn.2017.12.026.
Shi, Z., Z. Cheng, and H. Xiang. 2014. “Seismic isolation foundations with effective attenuation zones.” Soil Dyn. Earthq. Eng. 57 (Feb): 143–151. https://doi.org/10.1016/j.soildyn.2013.11.009.
Torshizi, M. F., M. Saitoh, G. M. Álamo, C. S. Goit, and L. A. Padrón. 2018. “Influence of pile radius on the pile head kinematic bending strains of end-bearing pile groups.” Soil Dyn. Earthquake Eng. 105 (Feb): 184–203. https://doi.org/10.1016/j.soildyn.2017.10.007.
Wagner, P. R., V. K. Dertimanis, E. N. Chatzi, and J. L. Beck. 2018. “Robust-to-uncertainties optimal design of seismic metamaterials.” J. Eng. Mech. 144 (3): 04017181. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001404.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 9 • September 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 16, 2018
Accepted: Jan 16, 2019
Published online: Jun 27, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 27, 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.