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Journal of Vibration Engineering & Technologies

, Volume 6, Issue 6, pp 513–521 | Cite as

Study of Two-Dimensional Acoustic Metamaterial Based on Lattice System

  • Sheng SangEmail author
  • Eric Sandgren
Original Paper
  • 5 Downloads

Abstract

Introduction

This article presents a comprehensive study of two-dimensional acoustic metamaterial based on mass-in-mass lattice model with both one resonator and multi-resonators. We demonstrate the dynamic anisotropic property of a two-dimensional lattice system and the existence of multiple stop bands of mass-in-mass lattice systems with more than one resonator.

Method

A two-dimensional stable lattice plate structure, composed of unit mass-in-mass cells is proposed, and been studied by adapting both an exact model and a continuum model.

Results

The dispersion surfaces and stop band obtained by the exact model show that the stop band of this metamaterial exists, and it can be shifted and operated upon. In contrast, the dispersion surface obtained through the continuum model describes the acoustic mode well, but is only accurate at low frequencies for the optical mode. By attaching a secondary resonator to the primary resonator, an additional stop band is achieved. Finally, an acoustic metamaterial plate which has more than one stop band is proposed and studied numerically. Good agreement has been achieved between theoretical and numerical analyses.

Keywords

Acoustic metamaterials Vibration Dispersion surface Stop band Continuum model 

References

  1. 1.
    Veselago VG (1968) The electrodynamics of substances with simultaneously negative values of e and l. Sov Phys Usp 10:509–514CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Chan CT, Li J, Fung KH (2006) On extending the concept of double negativity to acoustic waves. JZUS A 7:24–28CrossRefGoogle Scholar
  4. 4.
    Li J, Chan CT (2004) Double-negative acoustic metamaterial. Phys Rev E 70:055602CrossRefGoogle Scholar
  5. 5.
    Li J, Chan CT (2004) Double-negative Acoustic Metamaterial. Phys Rev E 70:055602(R)CrossRefGoogle Scholar
  6. 6.
    Milton GW, Willis JR (2007) On modifications of Newton’s second law and linear continuum elastodynamics. Proc R Soc A 463:855–880MathSciNetCrossRefGoogle 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.
    Pai P (2010) Metamaterial-based broadband elastic wave absorber. J Intell Mater Syst Struct 21(5):517–528CrossRefGoogle Scholar
  9. 9.
    Peng H, Pai PF (2014) Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression. Int J Mech Sci 89:350–361CrossRefGoogle Scholar
  10. 10.
    Pen H, Pai PF, Deng H (2015) Acoustic multi-stop band metamaterial plates design for broadband elastic wave absorption and vibration suppression. Int J Mech Sci 103:104–114CrossRefGoogle 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.
    Huang GL, Sun CT (2010) Stop bands in a multiresonator acoustic metamaterial. J Vibr Acoust 132:031003-1CrossRefGoogle Scholar
  13. 13.
    Huang HH, Sun CT (2009) Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. New J Phys 11:013003CrossRefGoogle Scholar
  14. 14.
    Liu AP, Zhu R, Liu XN, Hu GK, Huang GL (2012) Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials. Wave Motion 49:411–426CrossRefGoogle Scholar
  15. 15.
    Zhu R, Liu XN, Huang GL, Huang HH, Sun CT (2012) Microstructural design and experimental validation of elastic metamaterial plates with anisotropic mass density. Phys Rev B 86:144307CrossRefGoogle Scholar

Copyright information

© Krishtel eMaging Solutions Private Limited 2018

Authors and Affiliations

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

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