Study of In-Plane Wave Propagation in 2-Dimensional Anisotropic Elastic Metamaterials

  • Sheng SangEmail author
  • Eric Sandgren
Original Paper



Due to its multiple applications, elastic metamaterial is of great interest for researchers today. In this article, in-plane wave propagation in 2-D anisotropic metamateials with anisotropic density and anisotropic Young’s modulus is comprehensively studied.


Characteristics of wave propagation in 2-D metamaterial with different combinations of negative properties are provided, and the unnatural phenomenon is also explained. Based on Snell’s law and weld boundary condition, analysis of wave propagation from conventional isotropic material into anisotropic metamaterial is performed.


This paper can serve as a foundation for future study of massive modeling and simulation of both isotropic and anisotropic metamaterials.


Elastic metamaterials Wave propagation Anisotropy Christoffel equations Snell’s law 


  1. 1.
    Pao Yih-Hsing (1983) Elastic waves in solids. J Appl Mech 50(4b):1152–1164CrossRefGoogle Scholar
  2. 2.
    Yan X, Zhu R, Huang GL, Yuan FG (2013) Focusing flexural Lamb waves by designing elastic metamaterials welded on a plate. Health Monit Struct Biol Syst 103:12901Google Scholar
  3. 3.
    Bigoni D, Guenneau S, Movchan AB, Brun M (2013) Elastic metamaterials with inertial locally resonance structures: application to lensing and localization. Phys Rev B 87:174303CrossRefGoogle Scholar
  4. 4.
    Bongard F, Lissek H, Mosig JR (2010) Acoustic transmission line metamaterial with negative/zero/positive refractive index. Phys Rev B 82:094306CrossRefGoogle Scholar
  5. 5.
    Farhat M, Guenneau S, Enoch S (2009) Ultrabroadband elastic cloaking in thin plates. Phys Rev Lett 103:024301CrossRefGoogle Scholar
  6. 6.
    Zhu J, Christensen J, Jung J, Martin-Moreno L (2011) A holey-structured metamaterial for elastic deep-subwavelength imaging. Nat Phys 7:52–55CrossRefGoogle Scholar
  7. 7.
    Yao S, Zhou X, Hu G (2008) Experimental study on negative effective mass in a 1D mass-spring system. New J Phys 10:043020CrossRefGoogle Scholar
  8. 8.
    Wang Z, Lee S, Kim CK, Park CM, Nahm K, Nikitov SA (2008) Effective medium theory of the one-dimensional resonance phononic crystal. J Phys 20(5):055209Google Scholar
  9. 9.
    Huang GL, Sun CT (2010) Band gaps in a multiresonator acoustic metamaterial. J Vib Acoust 132:031003CrossRefGoogle Scholar
  10. 10.
    Huang HH, Sun CT (2009) Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. New J Phys 11:013003CrossRefGoogle Scholar
  11. 11.
    Huang HH, Sun CT, Huang GL (2009) On the negative effective mass density in acoustic metamaterials. Int J Eng Sci 47:610–617CrossRefGoogle Scholar
  12. 12.
    Cheng Y, Xu JY, Liu XJ (2008) One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Phys Rev B 77:045134CrossRefGoogle Scholar
  13. 13.
    Huang HH, Sun CT (2012) Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative density and Young’s modulus. J Acoust Soc Am 132:2887CrossRefGoogle Scholar
  14. 14.
    Li J, Chan CT (2004) Double-negative elastic metamaterial. Phys Rev E 70:055602CrossRefGoogle Scholar
  15. 15.
    Pai P (2010) Metamaterial-based broadband elastic wave absorber. J Intell Mater Syst Struct 21(5):517–528CrossRefGoogle Scholar
  16. 16.
    Peng H, Pai P (2014) Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression. Int J Mech Sci 89:350–361CrossRefGoogle Scholar
  17. 17.
    Pen H, Pai P, Deng H (2015) Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression. Int J Mech Sci 103:104–114CrossRefGoogle Scholar
  18. 18.
    Wu Y, Lai Y, Zhang Z (2011) Elastic metamaterials with simultaneously negative effective shear modulus and mass density. Phys Rev Lett 107:105506CrossRefGoogle Scholar
  19. 19.
    Liu XN, Hu GK, Sun CT, Huang GL (2011) Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. J Sound Vib 330:2536–2553CrossRefGoogle Scholar
  20. 20.
    Christensen J, García de Abajo FJ (2012) Anisotropic metamaterials for full control of acoustic waves. Phys Rev Lett 108:124301CrossRefGoogle Scholar
  21. 21.
    Torrent D, Sánchez-Dehesa J (2008) Anisotropic mass density by two-dimensional acoustic metamaterials. New J Phys 10:023004CrossRefGoogle Scholar
  22. 22.
    Sheng S, Eric S, Ziping W (2018) Wave attenuation and negative refraction of elastic waves in a single-phase elastic metamaterial. Acta Mechanica 229(6):2561–2569CrossRefGoogle Scholar
  23. 23.
    Gu Z, Jiang X, Liang B, Li Y, Zou X, Yin L, Cheng J (2015) Experimental realization of broadband acoustic directional absorber by homogeneous anisotropic metamaterials. J Appl Phys 117:074502CrossRefGoogle Scholar
  24. 24.
    Ao X, Chan CT (2008) Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials. Phys Rev E 77:025601CrossRefGoogle Scholar
  25. 25.
    Zhu R, Liu XN, Huang GL (2015) Study of anomalous wave propagation and reflection in semi-infinite elastic metamaterials. Wave Motion 55:73–83MathSciNetCrossRefGoogle Scholar
  26. 26.
    Rokhlin SI, Bolland TK, Adler L (1986) Reflection and reflection of elastic waves on a plane interface between two generally anisotropic media. J Acoust Soc Am 79:906CrossRefGoogle Scholar

Copyright information

© KrishteleMaging Solutions Private Limited 2019

Authors and Affiliations

  1. 1.Department of System EngineeringUniversity of Arkansas at Little RockLittle RockUSA

Personalised recommendations