Acta Mechanica Solida Sinica

, Volume 30, Issue 3, pp 271–284 | Cite as

A comparative study of wave localization in locally resonant Thue—Morse, Rudin—Shapiro and Period-Doubling aperiodic structures

Article

Abstract

The localization characteristics of the in-plane elastic waves in locally resonant aperiodic phononic crystals are examined in this study. In particular, the phononic crystals generated according to the Thue—Morse, Rudin—Shapiro and Period-Doubling sequences are theoretically investigated by using the extended transfer matrix method. For comparison, the binary and ternary locally resonant systems are considered, and their band structures are characterized by using the localization factors. Moreover, the influences of structural arrangement, material combination, incidence angle, number of components, length ratio, and random disorder on the band structures are also discussed. Some novel and interesting phenomena are observed and discussed.

Keywords

Phononic crystals Aperiodicity Wave localization Localization factor Transfer matrix method 

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References

  1. 1.
    M.M. Sigalas, C.M. Soukoulis, Elastic wave propagation through disordered and/or absorptive layered systems, Phys. Rev. B 51 (1995) 13961.CrossRefGoogle Scholar
  2. 2.
    M.M. Sigalas, E.N. Economou, Elastic and acoustic wave band structure, J. Sound Vib. 158 (1992) 377.CrossRefGoogle Scholar
  3. 3.
    M.S. Kushwaha, Classical band structure of periodic elastic composites, Int. J. Mod. Phys. B9 (1996) 977.CrossRefGoogle Scholar
  4. 4.
    Z. Liu, X.X. Zhang, Y.W. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Locally resonant sonic materials, Science 289 (2000) 1734.CrossRefGoogle Scholar
  5. 5.
    S.X. Yang, J.H. Page, Z.Y. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Focusing of sound in a 3D phononic crystal, Phys. Rev. Lett. 93 (2004) 024301.CrossRefGoogle Scholar
  6. 6.
    S.J. Martinez-Sala R, J.V. Sanchez, V. Gomez, J. Llinares, F. Meseguer, Sound attenuation by sculpture, Nature 378 (1995) pp. 241–241.CrossRefGoogle Scholar
  7. 7.
    Z.L. Hou, X.J. Fu, Y.Y. Liu, Calculational method to study the transmission properties of phononic crystals, Phys. Rev. B 70 (2004) 014304.CrossRefGoogle Scholar
  8. 8.
    Y. Tanaka, Y. Tomoyasu, S. Tamura, Band structure of acoustic waves in phononic lattices: two-dimensional composites with large acoustic mismatch, Phys. Rev. B 62 (2000) 7378–7392.CrossRefGoogle Scholar
  9. 9.
    M. Kafesaki, E.N. Economou, Multiple-scattering theory for three-dimensional periodic acoustic composites, Phys. Rev. B 60 (1999) 11993.CrossRefGoogle Scholar
  10. 10.
    J.O. Vasseur, P.A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost, Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals, Phys. Rev. Lett. 86 (2001) 3012.CrossRefGoogle Scholar
  11. 11.
    C. Goffaux, J. Sanchez-Dehesa, Two-dimensional phononic crystals studied using a variational method: application to lattices of locally resonant materials, Phys. Rev. B 67 (2003) 144301.CrossRefGoogle Scholar
  12. 12.
    G. Wang, J.H. Wen, Y.Y. Liu, Lumped-mass method for the study of band structure in two-dimensional phononic crystals, Phys. Rev. B 69 (2004) 184302.CrossRefGoogle Scholar
  13. 13.
    K. Bertoldi, L. Wang, Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures, Int. J. Solids Struct. 49 (2012) 2881–2885.CrossRefGoogle Scholar
  14. 14.
    J.J. Chen, Q. Wang, X. Han, Lamb wave transmission through one-dimensional three-component Fibonacci composite plates, Mod. Phys. Lett. B 24 (2010) 161–167.CrossRefGoogle Scholar
  15. 15.
    P.D. Sesion, E.I. Albuquerque, C. Chesman, V.N. Freire, Acoustic phonon transmission spectra in piezoelectric AlN/GaN Fibonacci phononic crystals, Eur. Phys. J. B 58 (2007) 379–387.CrossRefGoogle Scholar
  16. 16.
    P.D.C. King, T.J. Cox, Acoustic band gaps in periodically and quasiperiodically modulated waveguides, J. Appl. Phys. 102 (2007) 014902.CrossRefGoogle Scholar
  17. 17.
    H. Aynaou, E.H.EI. Boudouti, B Djafari-Rouhani, A Akjouj, V.R. Velasco, Propagation and localization of acoustic waves in Fibonacci phononic circuits, J. Phys. Condens. Matter. Phys. 17 (2005) 4245.CrossRefGoogle Scholar
  18. 18.
    L.C. Parsons, G.T. Andrews, Observation of hypersonic phononic crystal effects in porous silicon superlattices, Appl. Phys. Lett. 95 (2009) 241909.CrossRefGoogle Scholar
  19. 19.
    N.A. Gazi, G. Bernhard, Quasi-periodic Fibonacci and periodic one-dimensional hypersonic phononic crystals of porous silicon: experiment and simulation, J. Appl. Phys. 116 (2014) 094903.CrossRefGoogle Scholar
  20. 20.
    Z.Z. Yan, C.Z. Zhang, Y.S. Wang, Wave propagation and localization in randomly disordered layered composites with local resonances, Wave Motion 47 (2010) 409–420.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Z.Z. Yan, C.Z. Zhang, Band structures and localization properties of aperiodic layered phononic crystals, Physica B 407 (2012) 1014–1019.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingPR China
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany

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