Top

International Journal of Mechanics and Materials in Design

Published in:

16-08-2021

Ultra-wideband outward-hierarchical metamaterials with graded design

Authors: Xiao Liang, Fang Zhang, Jinhui Jiang

Published in: International Journal of Mechanics and Materials in Design | Issue 1/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The narrow band gap width caused by local resonance is the shackle for the further development of conventional metamaterials. In this paper, a novel type of hierarchical metamaterial containing parallel multiple resonators is presented, whose ultra-broadband vibration suppression property originates from a rational gradient design. Characterization of dispersion relations and bandgap characteristics of the one-dimensional outward-hierarchical lattice system reveals the variation of bandgap boundaries with relevant parameters. Thus, two gradient design approaches are proposed to overlap and merge the bandgaps. These designs are verified on the analogous continuum models by finite element simulations, and the ultra-wide wave/vibration attenuation band is consistent with the prediction of band gap diagram. Moreover, the range of the total band gap is determined by the boundary parameters of the gradient design, and its integrity is affected by the setting of gradient interval. In particular, the relationship between the gradient interval setting and the generation of overlapping gaps is analyzed. The gradient outward-hierarchical metamaterial is demonstrated to be an effective solution for elastic wave bandgap engineering, which can also be considered as a complement to existing inward-hierarchical configurations.

previous article Design of multi-channel bypass magnetorheological damper with three working modes

next article Phase-field simulation of multilayer microstructure of Cr-enriched phase induced by alternating strain

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Ambati, M., Fang, N., Sun, C., Zhang, X.: Surface resonant states and superlensing in acoustic metamaterials. Phys. Rev. B 75, 195447 (2007). https://doi.org/10.1103/PhysRevB.75.195447CrossRef

Arndt, E.M., Moore, W., Lee, W.K., Ortiz, C.: Mechanistic origins of bombardier beetle (Brachinini) explosion-induced defensive spray pulsation. Science 348(6234), 563–567 (2015). https://doi.org/10.1126/science.1261166CrossRef

Artigas, D., Torner, L.: Dyakonov surface waves in photonic metamaterials. Phys. Rev. Lett. 94(1), 013901 (2005). https://doi.org/10.1103/PhysRevLett.94.013901CrossRef

Babaee, S., Viard, N., Wang, P., Fang, N.X., Bertoldi, K.: Harnessing deformation to switch on and off the propagation of sound. Adv. Mater. (2016). https://doi.org/10.1002/adma.201504469CrossRef

Baravelli, E., Ruzzene, M.: Internally resonating lattices for bandgap generation and low-frequency vibration control. J. Sound Vib. 332(25), 6562–6579 (2013). https://doi.org/10.1016/j.jsv.2013.08.014CrossRef

Bilal, O.R., Foehr, A., Daraio, C.: Bistable metamaterial for switching and cascading elastic vibrations. Proc. Natl. Acad. Sci. USA 114(12), 201618314 (2017). https://doi.org/10.1073/pnas.1618314114CrossRef

Bodony, D.J., Day, L., Friscia, A.R., Fusani, L., Karon, A., Swenson, G.W., Wikelski, M., Schlinger, B.A.: Determination of the wingsnap sonation mechanism of the golden-collared manakin (Manacus vitellinus). J. Exp. Biol. 219(10), 1524–1534 (2016). https://doi.org/10.1242/jeb.128231CrossRef

Chen, H., Chan, C.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007). https://doi.org/10.1063/1.2803315CrossRef

Chen, Y., Wang, L.: Harnessing structural hierarchy to design stiff and lightweight phononic crystals. Extreme Mech. Lett. 9, 91–96 (2016). https://doi.org/10.1016/j.eml.2016.05.009CrossRef

Chen, J.J., Han, X., Li, G.Y.: Asymmetric lamb wave propagation in phononic crystal slabs with graded grating. J. Appl. Phys. 113, 184506 (2013). https://doi.org/10.1063/1.4804323CrossRef

Cheng, Y., Zhou, C., Yuan, B.G., Wu, D.J., Wei, Q., Liu, X.J.: Ultra-sparse metasurface for high reflection of low-frequency sound based on artificial Mie resonances. Nat. Mater. 14(10), 1013 (2015). https://doi.org/10.1038/nmat4393CrossRef

Chung, D.Y., Hogan, T., Brazis, P., Rocci-Lane, M., Kannewurf, C., Bastea, M., Uher, C., Kanatzidis, M.G.: CsBi4Te6: a high-performance thermoelectric material for low-temperature applications. Science 287(5455), 1024–1027 (2000). https://doi.org/10.1126/science.287.5455.1024CrossRef

Costas, M.: Soukoulis, martin wegener, past achievements and future challenges in 3D photonic metamaterials. Nat. Photonics 5(9), 523–530 (2011). https://doi.org/10.1038/nphoton.2011.154MathSciNetCrossRef

Cummer, S.A., Schurig, D.: One path to acoustic cloaking. New J. Phys. 9, 45 (2007). https://doi.org/10.1088/1367-2630/9/3/045CrossRef

Dughaish, Z.H.: Lead telluride as a thermoelectric material for thermoelectric power generation. Phys. B Condens. Matter 322, 205–223 (2002). https://doi.org/10.1016/S0921-4526(02)01187-0CrossRef

Gatt, R., Mizzi, L., Azzopardi, J.I., Azzopardi, K.M., Attard, D., Casha, A., Briffa, J., Grima, J.N.: Hierarchical auxetic mechanical metamaterials. Sci. Rep. 5, 8395 (2015). https://doi.org/10.1038/srep08395CrossRef

Han, H., Potyomina, L.G., Darinskii, A.A., Volz, S.: Phonon interference and thermal conductance reduction in atomic-scale metamaterials. Phys. Rev. B 89(18), 180301–180301 (2014). https://doi.org/10.1103/physrevb.89.180301CrossRef

Iwanaga, M.: Toward super-resolution imaging at green wavelengths employing stratified metal-insulator metamaterials. Photonics 2(2), 468–482 (2015). https://doi.org/10.3390/photonics2020468MathSciNetCrossRef

Krödel, S., Thomé, N., Daraio, C.: Wide band-gap seismic metastructures. Extreme Mech. Lett. 4, 111–117 (2015). https://doi.org/10.1016/j.eml.2015.05.004CrossRef

Li, J., Wang, W., Xie, Y., Popa, B., Cummer, S.A.: A sound absorbing metasurface with coupled resonators. J. Acoust. Soc. Am. 140(4), 2959–2959 (2016). https://doi.org/10.1063/1.4961671CrossRef

Lim, Q.J., Wang, P., Koh, S.J.A., Khoo, E.H., Bertoldi, K.: Wave propagation in fractal-inspired self-similar beam lattices. Appl. Phys. Lett. 107(22), 221911 (2015). https://doi.org/10.1063/1.4936564CrossRef

Liu, C., Reina, C.: Broadband locally resonant metamaterials with graded hierarchical architecture. J. Appl. Phys. 123, 095108 (2018). https://doi.org/10.1063/1.5003264CrossRef

Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. Science 289(5485), 1734–1736 (2000). https://doi.org/10.1126/science.289.5485.1734CrossRef

Liu, Na., Guo, H., Liwei, Fu., Kaiser, S., Schweizer, H., Giessen, H.: Three-dimensional photonic metamaterials at optical frequencies. Nat. Mater. 7(1), 31–37 (2008). https://doi.org/10.1038/nmat2072CrossRef

Liu, X.N., Hu, G.K., Huang, G.L., Sun, C.T.: An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl. Phys. Lett. 98, 251907 (2011). https://doi.org/10.1063/1.3597651CrossRef

Liu, Y., Su, X., Sun, C.T.: Broadband elastic metamaterial with single negativity by mimicking lattice systems. J. Mech. Phys. Solids 74, 158–174 (2015). https://doi.org/10.1016/j.jmps.2014.09.011CrossRef

Liu, C., Gao, W., Yang, B., Zhang, S.: Disorder-induced topological state transition in photonic metamaterials. Phys. Rev. Lett. 119(18), 183901 (2017). https://doi.org/10.1103/PhysRevLett.119.183901CrossRef

Lu, D., Liu, Z.: Hyperlenses and metalenses for far-field super-resolution imaging. Nat. Commun. 3, 1205 (2012). https://doi.org/10.1038/ncomms2176CrossRef

Lu, M.H., Feng, L., Chen, Y.F.: Phononic crystals and acoustic metamaterials. Mater. Today 12(12), 34–42 (2009). https://doi.org/10.1016/S1369-7021(09)70315-3CrossRef

Meng, H., Wen, J., Zhao, H., Wen, X.: Optimization of locally resonant acoustic metamaterials on underwater sound absorption characteristics. J. Sound Vib. 331(20), 4406–4416 (2012). https://doi.org/10.1016/j.jsv.2012.05.027CrossRef

Miniaci, M., Krushynska, A., Movchan, A.B., Bosia, F., Pugno, N.M.: Spider web-inspired acoustic metamaterials. Appl. Phys. Lett. 109(7), 071905 (2016). https://doi.org/10.1063/1.4961307CrossRef

Mousanezhad, D., Babaee, S., Ghosh, R., Mahdi, E., Bertoldi, K., Vaziri, A.: Honeycomb phononic crystals with self-similar hierarchy. Phys. Rev. B 92(10), 104304 (2015). https://doi.org/10.1103/PhysRevB.92.104304CrossRef

Nassar, H., Chen, H., Norris, A., Haberman, M., Huang, G.: Non-reciprocal wave propagation in modulated elastic metamaterials. Proc. R. Soc. A 473, 20170188 (2017). https://doi.org/10.1098/rspa.2017.0188MathSciNetCrossRefMATH

Oftadeh, R., Haghpanah, B., Vella, D., Boudaoud, A., Vaziri, A.: Optimal fractal-like hierarchical honeycombs. Phys. Rev. Lett. 113(10), 104301 (2014). https://doi.org/10.1103/PhysRevLett.113.104301CrossRef

Padilla, W.J., Taylor, A.J., Highstrete, C., Lee, M., Averitt, R.D.: Dynamical electric and magnetic metamaterial response at terahertz frequencies. Phys. Rev. Lett. 96, 107401 (2006). https://doi.org/10.1103/physrevlett.96.107401CrossRef

Pomot, L., Payan, C., Remillieux, M., Guenneau, S.: Acoustic cloaking: geometric transform, homogenization and a genetic algorithm. Wave Motion 102, 413 (2019). https://doi.org/10.1016/j.wavemoti.2019.102413CrossRefMATH

Popa, B.I., Cummer, S.A.: Non-reciprocal and highly nonlinear active acoustic metamaterials. Nat. Commun. 5, 3398 (2014). https://doi.org/10.1038/ncomms4398CrossRef

Rivera, J., Hosseini, M.S., Restrepo, D., Murata, S., Vasile, D., Parkinson, D.Y., Barnard, H.S., Arakaki, A., Zavattieri, P., Kisailus, D.: Toughening mechanisms of the elytra of the diabolical ironclad beetle. Nature 586, 543–548 (2020). https://doi.org/10.1038/s41586-020-2813-8CrossRef

Sersic, I., Frimmer, M., Verhagen, E., Femius Koenderink, A.: Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays. Phys. Rev. Lett. 103(21), 213902–213902 (2009). https://doi.org/10.1103/PhysRevLett.103.213902CrossRef

Tian, Y., Wu, J.H., Li, H., Gu, C., Yang, Z., Zhao, Z., Lu, K.: Elastic wave propagation in the elastic metamaterials containing parallel multi-resonators. J. Phys. D: Appl. Phys. 52(39), 395301 (2019). https://doi.org/10.1088/1361-6463/ab2dbaCrossRef

Tsouvalas, A.V.: Metrikine, noise reduction by the application of an air-bubble curtain in offshore pile driving. J. Sound Vib. 371, 150–170 (2016). https://doi.org/10.1016/j.jsv.2016.02.025CrossRef

Wang, Q., Jackson, J.A., Ge, Q., Hopkins, J.B., Spadaccini, C.M., Fang, N.X.: Lightweight mechanical metamaterials with tunable negative thermal expansion. Phys. Rev. Lett. 117, 175901 (2016). https://doi.org/10.1103/PhysRevLett.117.175901CrossRef

Watts, C.M., Liu, X., Padilla, W.J.: Metamaterial electromagnetic wave absorbers. Adv. Mater. 24, OP98-120 (2012). https://doi.org/10.1002/adma.201200674CrossRef

Xu, X.C., Barnhart, M.V., Li, X.P., Chen, Y.Y., Huang, G.L.: Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators. J. Sound Vib. 442, 237–248 (2019). https://doi.org/10.1016/j.jsv.2018.10.065CrossRef

Yang, B., Guo, Q., Tremain, B., Barr, L.E., Gao, W., Liu, H., Béri, B., Xiang, Y., Fan, D., Hibbins, A.P., Zhang, S.: Direct observation of topological surface-state arcs in photonic metamaterials. Nat. Commun. 8, 97 (2017). https://doi.org/10.1038/s41467-017-00134-1CrossRef

Yong, X., Wen, J., Wen, X.: Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. J. Sound Vib. 331(25), 5408–5423 (2012). https://doi.org/10.1016/j.jsv.2012.07.016CrossRef

Zeng, Yi., Yang, Xu., Deng, K., Peng, P., Yang, H., Muzamil, M., Qiujiao, Du.: A broadband seismic metamaterial plate with simple structure and easy realization. J. Appl. Phys. 125(22), 224901 (2019). https://doi.org/10.1063/1.5080693CrossRef

Zhang, P., To, A.C.: Broadband wave filtering of bioinspired hierarchical phononic crystal. Appl. Phys. Lett. 102(12), 121910 (2013). https://doi.org/10.1063/1.4799171CrossRef

Zhang, S., Yin, L., Fang, N.: Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009). https://doi.org/10.1103/PhysRevLett.102.194301CrossRef

Zhu, J., Chen, Y., Zhu, X., Garcia-Vidal, F.J., Yin, X., Zhang, W., Zhang, X.: Acoustic rainbow trapping. Sci. Rep. 3, 1728 (2013). https://doi.org/10.1038/srep01728CrossRef

Title: Ultra-wideband outward-hierarchical metamaterials with graded design
Authors: Xiao Liang
Fang Zhang
Jinhui Jiang
Publication date: 16-08-2021
Publisher: Springer Netherlands
Published in: International Journal of Mechanics and Materials in Design / Issue 1/2022
Print ISSN: 1569-1713
Electronic ISSN: 1573-8841
DOI: https://doi.org/10.1007/s10999-021-09565-7

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 1/2022

Global sensitivity analysis of electromechanical coupling behaviors for flexoelectric nanostructures

Numerical model of large spatial deflections of bundled conductors in electrical substations

Simplified robust and multiobjective optimization of piezoelectric energy harvesters with uncertain parameters

Instability and post-instability examination due to the buckling of rotating nanocomposite beams in thermal ambient

Message from the Editor-in-Chief

Analytical-geometrical percolation network model for piezoresistivity of hybrid CNT–CB polymer nanocomposites using Monte Carlo simulations

Premium Partners