Skip to main content
SpringerLink
Log in

The transmission properties of elastic waves through multilayers of spheres with planar defects

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The work presented in this paper discusses the transmission properties of elastic waves through multilayers of spheres which are periodically arranged in a homogeneous host material. The multilayers of spheres can have different kinds of planar defects. These defects are formed by removing one layer of spheres or by changing the radiuses or the material of scatterers in some layers. First, the reflection and transmission matrices of a single layer of spheres are obtained by the multiple scattering approaches and then the reflection and transmission matrices of multilayers of spheres are derived based on the polymerization method. Numerical examples are presented for 15 layers of spheres with one central planar defect layer or two symmetrically arranged planar defect layers. The influences of these planar defects on the frequency-dependent transmission curves are discussed. It is observed that the band gap can be widened evidently by introducing the planar defect, and the defect states appear in the band gap consequently. So the elaborately arranged planar defects are important in designing specific acoustic filters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Liu Z.Y., Chan C.T., Sheng P.: Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys. Rev. B 62, 2446–2457 (2000)

    Article  Google Scholar 

  2. Psarobas I.E., Stefanou N., Modinos A.: Scattering of elastic waves by periodic arrays of spherical bodies. Phys. Rev. B 62(1), 278–291 (2000)

    Article  Google Scholar 

  3. Liu Z., Chan C.T., Sheng P.: Three-component elastic wave band-gap material. Phys. Rev. B 65(16), 165116 (2002)

    Article  Google Scholar 

  4. Sainidou R., Stefanou N., Psarobas I.E. et al.: Scattering of elastic waves by a periodic monolayer of spheres. Phys. Rev. B 66(2), 024303 (2002)

    Article  Google Scholar 

  5. Sainidou R., Stefanou N., Psarobas I.E., Modinos A.: A layer-multiple-scattering method for phononic crystals and heterostructures of such. Comput. Phys. Commun. 166, 197–240 (2005)

    Article  Google Scholar 

  6. Wei P.J., Huang Z.P.: Dynamic effective properties of the particle-reinforced composites with the viscoelastic interphase. Int. J. Solids Struct. 41(24–25), 6993–7007 (2004)

    Article  MATH  Google Scholar 

  7. Wei P.J.: A self-consistent approach to the dynamic effective properties of composites reinforced by distributed spherical particles. Acta Mech. 185, 67–79 (2006)

    Article  MATH  Google Scholar 

  8. Fang X.Q., Wang D.B., Liu J.X.: Multiple scattering of elastic waves in metal–matrix composite materials with high volume concentration of particles. Eur. J. Mech. A/Solids 28, 377–386 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. James R., Woodley S.M., Dyer C.M. et al.: Sonic bands, bandgaps, and defect states in layered structures—theory and experiment. J. Acoust. Soc. Am. 97(4), 2041–2047 (1995)

    Article  Google Scholar 

  10. Munday J.N., Bennett C.B., Robson W.M.: Band gaps and defect modes in periodically structured waveguides. J. Acoust. Soc. Am. 112(4), 1353–1358 (2002)

    Article  Google Scholar 

  11. Robertson W.M., Baker C., Bennett C.B.: Slow group velocity propagation of sound via defect coupling in a one-dimensional acoustic band gap array. Am. J. Phys. 72(2), 255–257 (2004)

    Article  Google Scholar 

  12. Sigalas M.M.: Elastic wave band gaps and defect states in two-dimensional composites. J. Acoust. Soc. Am. 101(3), 1256–1261 (1997)

    Article  Google Scholar 

  13. Sigalas M.M.: Defects states of acoustic waves in a two-dimensional lattice of solid cylinders. J. Appl. Phys. 84(6), 3026–3030 (1998)

    Article  Google Scholar 

  14. Torres M., Montero de Espinosa F.R., García-Pablos D. et al.: Sonic band gaps in finite elastic media: Surface states and localization phenomena in linear and point defects. Phys. Rev. Lett. 82(15), 3054–3057 (1999)

    Article  Google Scholar 

  15. Kafesaki M., Sigalas M.M., García N.: Frequency modulation in transmittivity of wave guides in elastic-wave band-gap materials. Phys. Rev. Lett. 85(19), 4044–4047 (2000)

    Article  Google Scholar 

  16. Kafesaki M., Sigalas M.M., García N.: Wave guides in two-dimensional elastic wave band gap materials. Phys. B 296(1–3), 190–194 (2001)

    Article  Google Scholar 

  17. Wu F., Hou Z., Liu Z. et al.: Point defect states in two-dimensional phononic crystals. Phys. Lett. A 292(3), 198–202 (2001)

    Article  Google Scholar 

  18. Wu F.G., Liu Z.Y., Liu Y.Y.: Stop gaps and single defect states of acoustic waves in two-dimensional lattice of liquid cylinders. Chin. Phys. Lett. 18(6), 785–787 (2001)

    Article  Google Scholar 

  19. Wu F., Liu Z., Liu Y.: Splitting and tuning characteristics of the point defect modes in two-dimensional phononic crystals. Phys. Rev. E 69(6), 066608 (2004)

    Article  MathSciNet  Google Scholar 

  20. Chandra H., Deymier P.A., Vasseur J.O.: Elastic wave propagation along waveguides in three-dimensional phononic crystals. Phys. Rev. B 70(5), 054302 (2004)

    Article  Google Scholar 

  21. Pasrobas I.E., Stefanou N., Modinos A.: Phononic crystals with planar defects. Phys. Rev. B 62(9), 5536–5540 (2000)

    Article  Google Scholar 

  22. Zhao Q., Wei P.J.: The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement. Acta Mech. 224, 1009–1018 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing, 100083, China

    Qiang Zhao & P. J. Wei

  2. State Key Laboratory of Nonlinear Mechanics (LNM), Chinese Academy of Science, Beijing, Beijing, 100080, China

    P. J. Wei & Qiheng Tang

Authors
  1. Qiang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. J. Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiheng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. J. Wei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Q., Wei, P.J. & Tang, Q. The transmission properties of elastic waves through multilayers of spheres with planar defects. Acta Mech 227, 321–331 (2016). https://doi.org/10.1007/s00707-015-1392-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1392-5

Keywords

Search

Navigation