Acta Mechanica

, Volume 230, Issue 3, pp 1003–1008 | Cite as

A design of active elastic metamaterials with negative mass density and tunable bulk modulus

  • Sheng SangEmail author
  • Anwer Mhannawee
  • Ziping Wang
Original Paper


In this paper, a design of active elastic metamaterial that possesses negative density and tunable bulk modulus is presented for the negative refraction of in-plane elastic waves at deep subwavelength scale. The metamaterial is fabricated in an aluminum plate, and the resonant structure in a unit cell of the metamaterial composes of a coated steel that functions as a translational resonator and a radially polarized piezoelectric transducer shunted with negative capacitance. Based on effective continuum theory, the effective mass density and bulk modulus are numerically determined. The passive and active elements work together to generate broad band double-negative material properties. Simulation results verified and demonstrated the negative refraction of elastic waves at the interface between proposed elastic metamaterials and natural solids. The proposed elastic metamaterial may thus be used as a flat lens with broad working frequency regime for in-plane elastic wave focusing.


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  1. 1.
    Zhu, R., Liu, X.N., Hu, G.K., Sun, C.T., Huang, G.L.: Nat. Commun. 5, 5510 (2014)CrossRefGoogle Scholar
  2. 2.
    Sang, S., Wang, Z.: Acta Mech. 229, 2647 (2018)CrossRefGoogle Scholar
  3. 3.
    Sang, S., Sandgren, E., Wang, Z.: Acta Mech. 229, 2561 (2018)CrossRefGoogle Scholar
  4. 4.
    Ding, Y., Liu, Z., Qiu, C., Shi, J.: Phys. Rev. Lett. 99, 093904 (2007)CrossRefGoogle Scholar
  5. 5.
    Yan, X., Zhu, R., Huang, G.L., Yuan, F.G.: Appl. Phys. Lett. 103, 121901 (2013)CrossRefGoogle Scholar
  6. 6.
    Zhu, R., Chen, Y.Y., Barnhart, M.V., Hu, G.K., Sun, C.T., Huang, G.L.: Appl. Phys. Lett. 108, 011905 (2016)CrossRefGoogle Scholar
  7. 7.
    Behrens, S., Fleming, A.J., Moheimani, S.R.: Smart Mater. Struct. 12, 18–28 (2003)CrossRefGoogle Scholar
  8. 8.
    Park, C., Park, H.: J. Mech. Sci. Technol. 17, 1650–1658 (2003)Google Scholar
  9. 9.
    Chen, Y.Y., Huang, G.L.: Acta Mech. Sin. 31, 349–363 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, Y.Y., Hu, G.k, Huang, G.L.: J. Mech. Phys. Solids 105, 179–198 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Corr, L.R., Clark, W.W.: Smart Mater. Struct. 11, 370–376 (2002)CrossRefGoogle Scholar
  12. 12.
    Fleming, A.J., Belirens, S., Moheimani, S.O.R.: Electron. Lett. 36, 1525–1526 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Civil Engineering and MechanicsJiangsu UniversityZhenjiangChina
  2. 2.Department of Systems EngineeringUniversity of Arkansas at Little RockLittle RockUSA

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