Acta Mechanica Sinica

, Volume 31, Issue 3, pp 349–363 | Cite as

Active elastic metamaterials for subwavelength wave propagation control

  • Y. Y. Chen
  • G. L. HuangEmail author
Research Paper


Recent research activities in elastic metamaterials demonstrate a significant potential for subwavelength wave propagation control owing to their interior locally resonant mechanism. The growing technological developments in electro/magnetomechanical couplings of smart materials have introduced a controlling degree of freedom for passive elastic metamaterials. Active elastic metamaterials could allow for a fine control of material physical behavior and thereby induce new functional properties that cannot be produced by passive approaches. In this paper, two types of active elastic metamaterials with shunted piezoelectric materials and electrorheological elastomers are proposed. Theoretical analyses and numerical validations of the active elastic metamaterials with detailed microstructures are presented for designing adaptive applications in band gap structures and extraordinary waveguides. The active elastic metamaterial could provide a new design methodology for adaptive wave filters, high signal-to-noise sensors, and structural health monitoring applications.


Active elastic metamaterials Subwavelength wave control Adaptive metastructures Smart materials 



This work was supported by the Air Force Office of Scientific Research under Grant AF 9550-15-1-0061 with Program Manager Dr. Byung-Lip (Les) Lee.


  1. 1.
    Pendry, J.B., Holden, A.J., Robbins, D.J., et al.: Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999)CrossRefGoogle Scholar
  2. 2.
    Smith, D.R., Padilla, W.J., Vier, D.C., et al.: Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000)CrossRefGoogle Scholar
  3. 3.
    Liu, Z., Zhang, X., Mao, Y., et al.: Locally resonant sonic materials. Science 289, 1734–1736 (2000)CrossRefGoogle Scholar
  4. 4.
    Fang, N., Xi, D., Xu, J., et al.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452–456 (2006)CrossRefGoogle Scholar
  5. 5.
    Huang, H.H., Sun, C.T., Huang, G.L.: On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47, 610–617 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Yang, Z., Mei, J., Yang, M., et al.: Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301 (2008)CrossRefGoogle Scholar
  7. 7.
    Mei, J., Ma, G., Yang, M., et al.: Dark acoustic metamaterials as super absorbers for low-frequency sound. Nat. Commun. 3, 756 (2012)CrossRefGoogle Scholar
  8. 8.
    Liu, X.N., Hu, G.K., Huang, G.L., et al.: An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl. Phys. Lett. 98, 251907 (2011)CrossRefGoogle Scholar
  9. 9.
    Yan, X., Zhu, R., Huang, G.L., et al.: Focusing guided waves using surface bonded elastic metamaterials. Appl. Phys. Lett. 103, 121901 (2013)CrossRefGoogle Scholar
  10. 10.
    Wu, Y., Lai, Y., Zhang, Z.Q.: Elastic metamaterials with simultaneously negative effective shear modulus and mass density. Phys. Rev. Lett. 107, 105506 (2011)CrossRefGoogle Scholar
  11. 11.
    Zhu, R., Huang, G.L., Huang, H.H., et al.: Experimental and numerical study of guided wave propagation in a thin metamaterial plate. Phys. Lett. A 357, 2863–2867 (2011)CrossRefGoogle Scholar
  12. 12.
    Zhu, R., Liu, X.N., Hu, G.K., et al.: An chiral elastic metamaterial beam for broadband vibration suppression. J. Sound Vib. 333, 2759–2773 (2014)CrossRefGoogle Scholar
  13. 13.
    Forward, R.L.: Electronic damping of vibrations in optical structures. J. Appl. Opt. 18, 690–697 (1979)CrossRefGoogle Scholar
  14. 14.
    Hagood, N.W., Flotow, A.V.: Damping of structural vibrations with piezoelectric materials and passive electrical networks. J. Sound Vib. 146, 243–268 (1991)CrossRefGoogle Scholar
  15. 15.
    Wu, S.Y.: Method for multiple-mode shunt damping of structural vibration using a single PZT transducer. In: Proceedings of SPIE smart structures and materials, smart structures and intelligent systems, Huntington Beach, CA (1998)Google Scholar
  16. 16.
    Wu, S.Y., Bicos, A.S.: Structural vibration damping experiments using improved piezoelectric shunts. In: Proceedings of SPIE smart structures and materials, San Diego, CA, 3–5 March, 40–50 (1997)Google Scholar
  17. 17.
    Corr, L.R., Clark, W.W.: Comparison of low-frequency piezoelectric switching shunt techniques for structural damping. Smart Mater. Struct. 11, 370–376 (2002)CrossRefGoogle Scholar
  18. 18.
    Fleming, A.J., Belirens, S., Moheimani, S.O.R.: Synthetic impedance for implementation of piezoelectric shunt damping circuits. Electron. Lett. 36, 1525–1526 (2000)CrossRefGoogle Scholar
  19. 19.
    Behrens, S., Fleming, A.J., Moheimani, S.R.: A broadband controller for shunt piezoelectric damping of structural vibration. Smart Mater. Struct. 12, 18–28 (2003)CrossRefGoogle Scholar
  20. 20.
    Park, C., Park, H.: Multiple-mode structural vibration control using negative capacitive shunt damping. J. Mech. Sci. Technol. 17, 1650–1658 (2003)Google Scholar
  21. 21.
    Beck, B., Cunefare, K., Ruzzene, M., et al.: Experimental analysis of a cantilever beam with a shunted piezoelectric periodic array. J. Intell. Mater. Syst. Struct. 22, 1177–1187 (2011)CrossRefGoogle Scholar
  22. 22.
    Park, C.H., Baz, A.: Vibration control of beams with negative capacitive shunting of interdigital electrode piezoceramics. J. Vib. Control 11, 331–346 (2005)zbMATHCrossRefGoogle Scholar
  23. 23.
    Date, M., Kutani, M., Sakai, S.: Electrically controlled elasticity utilizing piezoelectric coupling. J. Appl. Phys. 87, 863 (2000)Google Scholar
  24. 24.
    Imoto, K., Nishiura, M., Yamamoto, K., et al.: Elasticity control of piezoelectric lead zirconate titanate (PZT) materials using negative-capacitance circuits. Jpn. J. Appl. Phys. 44, 7019–7023 (2005)CrossRefGoogle Scholar
  25. 25.
    Chen, S.B., Wen, J.H., Yu, D.L., et al.: Band gap control of phononic beam with negative capacitance piezoelectric shunt. Chin. Phys. B 20, 014301 (2011)CrossRefGoogle Scholar
  26. 26.
    Chen, S.B., Wen, J.H., Wang, G., et al.: Tunable band gaps in acoustic metamaterials with periodic arrays of resonant shunted piezos. Chin. Phys. B 22, 074301 (2013)CrossRefGoogle Scholar
  27. 27.
    Chen, S.B., Wang, G., Wen, J.H., et al.: Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches. J. Sound Vib. 332, 1520–1532 (2013)CrossRefGoogle Scholar
  28. 28.
    Casadei, F., Delpero, T., Bergamini, A., et al.: Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials. J. Appl. Phys. 112, 064902 (2012)CrossRefGoogle Scholar
  29. 29.
    Airoldi, L., Ruzzene, M.: Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos. New J. Phys. 13, 113010 (2011)CrossRefGoogle Scholar
  30. 30.
    Ginder, J.M., Nichols, M.E., Elie, L.D., et al.: Magnetorheological elastomers: properties and applications. Proc. SPIE 3675, 131–138 (1999)Google Scholar
  31. 31.
    Li, W.H., Zhang, X.Z.: A study of the magnetorheological effect of bimodal particle based magnetorheological elastomers. Smart Mater. Struct. 19, 035002 (2010)CrossRefGoogle Scholar
  32. 32.
    Xu, Z.B., Gong, X.L., Liao, G.J., et al.: An active damping-compensated magnetorheological elastomer adaptive tuned vibration absorber. J. Intell. Mater. Syst. Struct. 21, 1039–1047 (2010)Google Scholar
  33. 33.
    Liao, G.J., Gong, X.L., Xuan, S.H., et al.: Development of a real-time tunable stiffness and damping vibration isolator based on magnetorheological elastomer. J. Intell. Mater. Syst. Struct. 23, 25–33 (2012)CrossRefGoogle Scholar
  34. 34.
    Liao, G.J., Gong, X.L., Xuan, S.H.: Phase based stiffness tuning algorithm for a magnetorheological elastomer dynamic vibration absorber. Smart Mater. Struct. 23, 015016 (2014)CrossRefGoogle Scholar
  35. 35.
    Xu, Z., Wu, F.: Elastic band gaps of magnetorheological elastomer vibration isolators. J. Intell. Mater. Syst. Struct. 10, 14535014 (2014)Google Scholar
  36. 36.
    Tang, H., Luo, C., Zhao, X.: Tunable characteristics of a flexible thin electrorheological layer for low frequency acoustic waves. J. Phys. D: Appl. Phys. 37, 2331–2336 (2004)CrossRefGoogle Scholar
  37. 37.
    Yeh, J.Y.: Control analysis of the tunable phononic crystal with electrorheological material. Phys. B: Condens. Matter 400, 137–144 (2007)CrossRefGoogle Scholar
  38. 38.
    Zhou, X.L., Chen, C.Q.: Tuning the locally resonant phononic band structures of two-dimensional periodic electroactive composites. Phys. B: Condens. Matter. 431, 23–31 (2013)Google Scholar
  39. 39.
    Chen, Y.Y., Huang, G.L., Sun, C.T.: Band gap control in an active elastic metamaterial with negative capacitance piezoelectric shunting. J. Vib. Acoust. 136, 061008 (2014)CrossRefGoogle Scholar
  40. 40.
    Guo, N., Cawley, P.: The interaction of Lamb waves with delaminations in composite laminates. J. Acoust. Soc. Am. 94, 2240–2246 (1993)CrossRefGoogle Scholar
  41. 41.
    Lemistre, M., Balageas, D.: Structural health monitoring system based on diffracted Lamb wave analysis by multiresolution processing. Smart Mater. Struct. 10, 504–511 (2001)CrossRefGoogle Scholar
  42. 42.
    Liu, B., Shaw, M.T.: Electrorheology of filled silicone elastomers. J. Rheol. 45, 641–657 (2001)CrossRefGoogle Scholar
  43. 43.
    Hu, J., Chang, Z., Hu, G.K.: Approximate method for controlling solid elastic waves by transformation media. Phys. Rev. B 84, 201101(R) (2011)CrossRefGoogle Scholar
  44. 44.
    Chang, Z., Hu, J., Hu, G.K., et al.: Controlling elastic waves with isotropic materials. Appl. Phys. Lett. 98, 121904 (2011)CrossRefGoogle Scholar
  45. 45.
    Wu, T.T., Chen, Y.T., Sun, J.H., et al.: Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate. Appl. Phys. Lett. 98, 171911 (2011)CrossRefGoogle Scholar
  46. 46.
    Schiller, N.H., Lin, S.C.S., Cabell, R.H., et al.: Design of a variable thickness plate to focus bending waves. In: ASME 2012 Noise Control and Acoustics Division Conference, New York City, New York, USA (2012)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaUSA

Personalised recommendations