Skip to main content
SpringerLink
Log in

Modulation of the Band Gaps of Phononic Crystals with Thermal Effects

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

Band gaps of elastic waves, both in-plane and shear waves, propagating through one-dimensional perfect/defect phononic crystals (PnCs) that involve thermal effects are studied in this paper. Based on the transfer matrix method and Bloch theory, the expressions of the reflection coefficients and dispersion relation are presented. Elastic waves localization is obtained by immersing a defect layer through a perfect structure. Compared with the periodic structure, we observed that defected PnCs introduced localized modes or peaks within the phononic band gaps. Hence, Numerical simulations are performed to investigate the influences of the defect layer thickness and type on the number and intensity of the localized modes. Moreover, we have observed that temperature changes have prominent effects on the localized modes and band gaps width, especially at plane wave propagation. Such effects could change thermal properties of the PnCs structure such as thermal conductivity and could control the thermal emission contributed by phonons in many engineering structures.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. T. Gorishyy, M. Maldovan, C. Ullal, E. Thomas, Sound ideas. Phys. World 18(2), 24–29 (2005)

    Article  Google Scholar 

  2. M.N. Armenise, C.E. Campanella, C. Ciminelli, F. dell’Olio, V.M.N. Passro, Photonic and phononic band gap structures: modeling and applications. Phys. Procedia 3, 357–364 (2010)

    Article  ADS  Google Scholar 

  3. D. Torrent, J. Sanchez-Dehesa, Radial wave crystals: radially periodic structures from anisotropic metamaterials for engineering acoustic or electromagnetic waves. Phys. Rev. Lett. 103(064301), 1–4 (2009)

    Google Scholar 

  4. L. Fok, X. Zhang, Negative acoustic index metamaterial. Phys. Rev. B 83(214304), 1–8 (2011)

    Google Scholar 

  5. I. El- Kady, R. H. Olsson III, P. E. Hopkins, Z. C. Leseman, D. F. Goettler, B. Kim, M. R. Charles, F. Su. Mehmet, Phonon Manipulation with Phononic Crystals, Sandia National laboratories, SAND-0127 (2012)

  6. L.Y. Wu, W.P. Yang, L.W. Chen, The thermal effects on the negative refraction of sonic crystals. Phys. Lett. A 372, 2701–2705 (2008)

    Article  ADS  Google Scholar 

  7. P. E. Hopkins, L. M. Phinney, P. T. Rakich, R. H. Olsson III, I. EL-Kady, Phonon considerations in the reduction of thermal conductivity in phononic crystals. In: MeTA’10 2\(^{\rm nd}\) International conference on metamaterials, photonic crystals and plasmonics, pp. 308–316 (2010)

  8. A.L. Chen, Y.-S. Wang, Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals. Physica B 392, 369–378 (2007)

    Article  ADS  Google Scholar 

  9. C. Racknor, M.R. Singh, Y. Zhang, D.J.S. Birch, Y. Chen, Energy transfer between a biological labeling dye and gold nanorods. Methods Appl. Fluoresc. 2(1), 015002 (2014)

    Article  ADS  Google Scholar 

  10. J.L. Rose, Ultrasonic Waves in Solid Media (Cambridge University Press, London, 1999)

    Google Scholar 

  11. Y.Z. Wang, F.M. Li, K. Kishimoto, Y.H. Wang, W.H. Huang, Wave localization in randomly disordered layered three-component phononic crystals with thermal effects. Arch. Appl. Mech. 80, 629–640 (2010)

    Article  MATH  ADS  Google Scholar 

  12. F.L. Shang, Z.K. Wang, Z.H. Li, An exact analysis of thermal buckling of piezoelectric laminated plates. Acta Mech. Solida Sin. 10, 95–107 (1997)

    Google Scholar 

  13. F.M. Li, Y.S. Wang, Study on wave localization in disordered periodic layered piezoelectric composite structures. Int. J. Solids Struct. 42, 6457–6474 (2005)

    Article  MATH  Google Scholar 

  14. M.I. Hussein, G.M. Hulbert, R.A. Scott, Dispersive elastodynamics of 1D banded materials and structures: analysis. J. Sound Vib. 289, 779–806 (2006)

    Article  ADS  Google Scholar 

  15. A.H. Aly, A. Mehaney, Enhancement of phononic band gaps in ternary/binary structure. Phys. B: Condens. Matter 407(21), 4262–4268 (2012)

    Article  ADS  Google Scholar 

  16. D.E. Gray, D.N. Fischel, H.B. Crawford, D.A. Douglas, W.C. Eisler, American Institute of Physics Handbook, 3rd edn. (Colonial Press, McGraw-Hill Book Company, New York, 1972)

    Google Scholar 

  17. W.P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics (D. Van Nostrand Company Inc, Princeton, NJ, 1950), pp. 480–481

    Google Scholar 

  18. R.A. Serway, J.W. Jewett, Physics for Scientists and Engineers, 6th edn. (Thomson Brooks/Cole, Belmont, 2004)

    Google Scholar 

  19. A.H. Aly, A. Mehaney, E. Abdel-Rahman, Study of physical parameters on the properties of phononic band gaps. Int. J. Mod. Phys. B 27, 1350047 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  20. C. Ciminelli, F. Peluso, M.N. Armenise, Modelling and design of two-dimensional guided-wave photonic band-gap devices. J. Light Wave Technol. 23, 886–901 (2005)

    Article  ADS  Google Scholar 

  21. M. Maldovan, E.L. Thomas, Periodic Materials and Interference Lithography for Photonics, Phononics and Mechanics (Wiley-vch Verlag GmbH and Company KGaA, Weinheim, 2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Faculty of Sciences, Beni-Suef University, Beni Suef, Egypt

    Arafa H. Aly & Ahmed Mehaney

Authors
  1. Arafa H. Aly
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed Mehaney
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arafa H. Aly.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aly, A.H., Mehaney, A. Modulation of the Band Gaps of Phononic Crystals with Thermal Effects. Int J Thermophys 36, 2967–2984 (2015). https://doi.org/10.1007/s10765-015-1952-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-015-1952-x

Keywords

Search

Navigation