Acta Mechanica

, Volume 230, Issue 12, pp 4453–4461 | Cite as

Wave propagation in one-dimensional infinite acoustic metamaterials with long-range interactions

  • Esmaeal GhavanlooEmail author
  • S. Ahmad Fazelzadeh
Original Paper


In this paper, the effect of long-range interactions on the wave propagation in one-dimensional acoustic metamaterials is investigated. The wave dispersion relations of these materials are expressed in closed-form solutions. In addition, a nonlocal continuum model is developed to approximate the behavior of the metamaterials with general long-range interactions. The influences of various parameters including the mass and stiffness ratios are also examined. The numerical results show that the long-range interactions affect the shape of the dispersion curves, while the range of the band-gap slightly changes. Furthermore, the results indicate that the proposed nonlocal model with appropriate nonlocal parameters can predict the dispersion behavior of the one-dimensional mass-in-mass system with long-range interactions very well, especially for the acoustic mode.



  1. 1.
    Zhu, R., Huang, H.H., Huang, G.L., Sun, C.T.: Microstructure continuum modeling of an elastic metamaterial. Int. J. Eng. Sci. 49, 1477–1485 (2011)CrossRefGoogle Scholar
  2. 2.
    Wang, X.: Dynamic behaviour of a metamaterial system with negative mass and modulus. Int. J. Solids Struct. 51, 1534–1541 (2014)CrossRefGoogle Scholar
  3. 3.
    He, Z.C., Li, E., Wang, G., Li, G.Y., Xia, Z.: Development of an efficient algorithm to analyze the elastic wave in acoustic metamaterials. Acta Mech. 227, 3015–3030 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Zhou, X., Hu, G.: Dynamic effective models of two-dimensional acoustic metamaterials with cylindrical inclusions. Acta Mech. 224, 1233–1241 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Sang, S., Sandgren, E.: Study of two-dimensional acoustic metamaterial based on lattice system. J. Vib. Eng. Technol. 6, 513–521 (2018)CrossRefGoogle Scholar
  6. 6.
    Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. Science 289, 1734–1736 (2000)CrossRefGoogle Scholar
  7. 7.
    Zhou, X., Liu, X., Hu, G.: Elastic metamaterials with local resonances: an overview. Theor. Appl. Mech. Lett. 2, 041001 (2012)CrossRefGoogle Scholar
  8. 8.
    Zhu, R., Liu, X.N., Hu, G.K., Yuan, F.G., Huang, G.L.: Microstructural designs of plate-type elastic metamaterial and their potential applications: a review. Int. J. Smart Nano Mater. 6, 14–40 (2015)CrossRefGoogle Scholar
  9. 9.
    Cselyuszka, N., Sĕcujski, M., Crnojević-Bengin, V.: Novel negative mass density resonant metamaterial unit cell. Phys. Lett. A 379, 33–36 (2015)CrossRefGoogle Scholar
  10. 10.
    Sang, S., Wang, Z.: A design of elastic metamaterials with multi-negative pass bands. Acta Mech. 229, 2647–2655 (2018)CrossRefGoogle Scholar
  11. 11.
    Beli, D., Arruda, J.R.F., Ruzzene, M.: Wave propagation in elastic metamaterial beams and plates with interconnected resonators. Int. J. Solids Struct. 139–140, 105–120 (2018)CrossRefGoogle Scholar
  12. 12.
    Yao, S., Zhou, X., Hu, G.: Experimental study on negative mass effective mass in a 1D mass-spring system. New J. Phys. 10, 043020 (2008)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Huang, G.L., Sun, C.T.: Band gaps in a multiresonator acoustic metamaterial. J. Vib. Acoust. 132, 031003 (2010)CrossRefGoogle Scholar
  15. 15.
    Manimala, J.M., Huang, H.H., Sun, C.T., Snyder, R., Bland, S.: Dynamic load mitigation using negative effective mass structures. Eng. Struct. 80, 458–468 (2014)CrossRefGoogle Scholar
  16. 16.
    Fang, X., Wen, J., Yin, J., Yu, D.: Wave propagation in nonlinear metamaterial multi-atomic chains based on homotopy method. AIP Adv. 6, 121706 (2016)CrossRefGoogle Scholar
  17. 17.
    Fang, X., Wen, J., Bonello, B., Yin, J., Yu, D.: Wave propagation in one-dimensional nonlinear acoustic metamaterials. New J. Phys. 19, 053007 (2017)CrossRefGoogle Scholar
  18. 18.
    Terao, T.: Wave propagation in acoustic metamaterial double-barrier structures. Phys. Status Solidi A 213, 2773–2779 (2016)CrossRefGoogle Scholar
  19. 19.
    Kulkarni, P.P., Manimala, J.M.: Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials. J. Appl. Phys. 119, 245101 (2016)CrossRefGoogle Scholar
  20. 20.
    Hu, G., Tang, L., Das, R., Gao, S., Liu, H.: Acoustic metamaterials with coupled local resonators for broadband vibration suppression. AIP Adv. 7, 025211 (2017)CrossRefGoogle Scholar
  21. 21.
    Banerjee, A., Das, R., Calius, E.P.: Frequency graded 1D metamaterials: a study on the attenuation bands. J. Appl. Phys. 122, 075101 (2017)CrossRefGoogle Scholar
  22. 22.
    Al Ba’ba’a, H.B., Nouh, M.: Mechanics of longitudinal and flexural locally resonant elastic metamaterials using a structural power flow approach. Int. J. Mech. Sci. 122, 341–354 (2017)CrossRefGoogle Scholar
  23. 23.
    Cveticanin, L., Zukovic, M.: Negative effective mass in acoustic metamaterial with nonlinear mass-in-mass subsystems. Commun. Nonlinear Sci. Numer. Simul. 51, 89–104 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Cveticanin, L., Zukovic, M., Cveticanin, D.: On the elastic metamaterial with negative effective mass. J. Sound Vib. 436, 295–309 (2018)CrossRefGoogle Scholar
  25. 25.
    Li, B., Alamri, S., Tan, K.T.: A diatomic elastic metamaterial for tunable asymmetric wave transmission in multiple frequency bands. Sci. Rep. 7, 6226 (2017)CrossRefGoogle Scholar
  26. 26.
    Comi, C., Driemeier, L.: Wave propagation in cellular locally resonant metamaterials. Lat. Am. J. Solids Struct. 15, e38 (2018)CrossRefGoogle Scholar
  27. 27.
    Xu, X., Barnhart, M.V., Li, X., Chen, Y., Huang, G.: Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators. J. Sound Vib. 442, 237–248 (2019)CrossRefGoogle Scholar
  28. 28.
    Ponge, M.F., Poncelet, O., Torrent, D.: Dynamic homogenization theory for nonlocal acoustic metamaterials. Extreme Mech. Lett. 12, 71–76 (2017)CrossRefGoogle Scholar
  29. 29.
    Bacquet, C.L., Al Ba’ba’a, H., Frazier, M.J., Nouh, M., Hussein, M.I.: Metadamping: dissipation emergence in elastic metamaterials. Adv. Appl. Mech. 51, 115–164 (2018)CrossRefGoogle Scholar
  30. 30.
    Carcaterra, A., Coppo, F., Mezzani, F., Pensalfini, S.: Long-range retarded elastic metamaterials: wave-stopping, negative, and hypersonic or superluminal group velocity. Phys. Rev. Appl. 11, 014041 (2019)CrossRefGoogle Scholar
  31. 31.
    Zhou, Y., Wei, P., Tang, Q.: Continuum model of a one-dimensional lattice of metamaterials. Acta Mech. 227, 2361–2376 (2016)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Ghavanloo, E., Rafii-Tabar, H., Fazelzadeh, S.A.: Computational Continuum Mechanics of Nanoscopic Structures: Nonlocal Elasticity Approaches. Springer, Berlin (2019)CrossRefGoogle Scholar
  33. 33.
    Al Ba’ba’a, H., Nouh, M., Singh, T.: Formation of local resonance band gaps in finite acoustic metamaterials: a closed-form transfer function model. J. Sound Vib. 410, 429–446 (2017)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShiraz UniversityShirazIran

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