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A design of elastic metamaterials with multi-negative pass bands

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Abstract

In this paper, an elastic metamaterial is proposed by integrating a two-dimensionally periodic honeycomb lattice and tetrachiral metamaterial inclusions for low-frequency wave applications. Plane wave propagation in infinite periodic cells is investigated through using Floquet–Bloch principles and the finite element method. Two separate negative pass bands induced by different mechanisms appear in the band structures of wave propagation in the proposed elastic metamaterial. The working mechanisms of those two negative pass bands are revealed though analyzing the eigenmodes of the unit cell and the dynamic effective material properties. Numerical examples validate the proposed model and show that negative refraction of elastic waves in the elastic metamaterial has been obtained. The design concept of this type of elastic may be of use for the design of broadband flat lenses for elastic wave focusing.

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References

  1. Veselago, V.G.: The electrodynamics of substances with simultaneously negative values of \(\varepsilon \) and \(\mu \). Sov. Phys. Uspekhi 10, 509–514 (1968)

    Article  Google Scholar 

  2. Shelby, R.A., Smith, D.R., Shultz, S.: Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)

    Article  Google Scholar 

  3. Pendry, J.B.: A chiral route to negative refraction. Science 19, 1353–1355 (2004)

    Article  Google Scholar 

  4. Luo, C., Johnson, S.G., Joannopoulos, J.D., Pendry, J.B.: All-angle negative refraction without negative effective index. Phys. Rev. B 65, 201104 (2002)

    Article  Google Scholar 

  5. Yao, J., Liu, Z., Liu, Y., Wang, Y., Sun, C., Bartal, G., Stacy, A.M., Zhang, X.: Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930 (2008)

    Article  Google Scholar 

  6. Cubukcu, E., Aydin, K., Ozbay, E., Foteinopoulou, S., Soukoulis, C.M.: Electromagnetic waves: negative refraction by photonic crystals. Nature 423, 604–605 (2003)

    Article  Google Scholar 

  7. Smith, D.R., Pendry, J.B., Wiltshire, M.C.K.: Metamaterials and negative refractive index. Science 305, 788–792 (2004)

    Article  Google Scholar 

  8. Padilla, W.J., Smith, D.R., Basov, D.N.: Spectroscopy of metamaterials from infrared to optical frequencies. J. Opt. Soc. Am. B 23, 404–414 (2006)

    Article  Google Scholar 

  9. Ding, Y., Liu, Z., Qiu, C., Shi, J.: Metamaterial with simultaneously negative bulk modulus and mass density. Phys. Rev. Lett. 99, 093904 (2007)

    Article  Google Scholar 

  10. Lai, Y., Wu, Y., Sheng, P., Zhang, Z.Q.: Hybrid elastic solids. Nat. Mater. 10, 620–624 (2011)

    Article  Google Scholar 

  11. Wu, Y., Lai, Y., Zhang, Z.Q.: Elastic metamaterials with simultaneously negative effective shear modulus and mass density. Phys. Rev. Lett. 107, 105506 (2011)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Pope, S.: Double negative elastic metamaterial design through electrical-mechanical circuit analogies. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 1467–1474 (2013)

    Article  Google Scholar 

  14. Wang, X.: Dynamic behavior of a metamaterial system with negative mass and modulus. Int. J. Solids Struct. 51, 1534–1541 (2014)

    Article  Google Scholar 

  15. Li, Z., Wang, X.: On the dynamic behavior of a two dimensional elastic metamaterial system. Int. J. Solids Struct. 78–79, 174–181 (2016)

    Article  Google Scholar 

  16. Zhu, R., Liu, X.N., Hu, G.K., Sun, C.T., Huang, G.L.: NR of elastic waves at the deep-subwavelength scale in a single-phase metamaterial. Nat. Commun. 5, 5510 (2014)

    Article  Google Scholar 

  17. Phani, A.S., Woodhouse, J., Fleck, N.A.: Wave propagation in two-dimensional periodic lattices. J. Acoust. Soc. Am. 119, 1995–2005 (2006)

    Article  Google Scholar 

  18. Åberg, M., Gudmundson, P.: The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure. J. Acoust. Soc. Am. 102, 2007–2013 (1997)

    Article  Google Scholar 

  19. Liu, X.N., Hu, G.K., Huang, G.L., Sun, C.T.: Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. J. Sound Vib. 330, 2536–2553 (2011)

    Article  Google Scholar 

  20. Zhu, R., Liu, X.N., Hu, G.K., Sun, C.T., Huang, G.L.: A chiral EMM beam for broadband vibration suppression. J. Sound Vib. 333, 2759–2773 (2014)

    Article  Google Scholar 

  21. Huang, G.L., Sun, C.T.: Band gaps in a multiresonator acoustic metamaterial. ASME J. Vib. Acoust. 132, 031003 (2010)

    Article  Google Scholar 

  22. Pai, P.F.: Metamaterial-based broadband elastic wave absorber. J. Intell. Mater. Syst. Struct. 21, 517–528 (2010)

    Article  Google Scholar 

  23. Sun, H.W., Du, X.W., Pai, P.F.: Theory of metamaterial beams for broadband vibration absorption. J. Intell. Mater. Syst. Struct. 21, 1085–1101 (2010)

    Article  Google Scholar 

  24. Xiao, Y., Wen, J., Wen, X.: Broadband locally resonant beams containing multiple periodic arrays of attached resonators. Phys. Lett. A 376, 1384–1390 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The work carried out in this report is partially funded and supported by National Natural Science Foundation of China (Grants No. 11402101).

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Authors and Affiliations

  1. Department of System Engineering, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Sheng Sang

  2. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, China

    Sheng Sang & Ziping Wang

Authors
  1. Sheng Sang
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  2. Ziping Wang
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Correspondence to Sheng Sang.

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Sang, S., Wang, Z. A design of elastic metamaterials with multi-negative pass bands. Acta Mech 229, 2647–2655 (2018). https://doi.org/10.1007/s00707-018-2128-0

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  • DOI: https://doi.org/10.1007/s00707-018-2128-0

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