Advertisement

Acta Mechanica Solida Sinica

, Volume 19, Issue 1, pp 50–57 | Cite as

Wave localization in randomly disordered periodic piezoelectric rods

  • Fengming Li
  • Yuesheng Wang
  • Ali Chen
Article

Abstract

The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.

Key words

periodic piezoelectric rod wave localization transfer matrix localization factor disorder 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Crawley, E.F., Intelligent structures for aerospace: a technology overview and assessment, AIAA Journal, Vol.32, 1994, 1689–1699.CrossRefGoogle Scholar
  2. [2]
    Nie, R.T., Shao, C.X. and Zou, Z.Z., Mech-electric coupling dynamic analysis and vibration control of intelligent truss structures, Journal of Vibration Engineering, Vol.10, No.2, 1997, 119–124 (in Chinese).Google Scholar
  3. [3]
    Baz, A., Active control of periodic structures, ASME, Journal of Vibration and Acoustics, Vol.123, 2001, 472–479.CrossRefGoogle Scholar
  4. [4]
    Thorp, O., Ruzzene, M. and Baz, A., Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches, Smart Materials and Structures, Vol.10, 2001, 979–989.CrossRefGoogle Scholar
  5. [5]
    Li, F.M., Hu, C., Huang, W.H. and Zhou, M., Wave localization in disordered multi-span beams with elastic supports, Acta Mechanica Solida Sinica, Vol.25, No.1, 2004, 83–86 (in Chinese).CrossRefGoogle Scholar
  6. [6]
    Li, F.M., Wang, Y.S., Hu, C. and Huang, W.H., Localization of elastic waves in periodic rib-stiffened rectangular plates under axial compressive load, Journal of Sound and Vibration, Vol.281, 2005, 261–273.CrossRefGoogle Scholar
  7. [7]
    Li, F.M. and Wang, Y.S., Study on wave localization in disordered periodic layered piezoelectric composite structures, International Journal of Solids and Structures, Vol.42, 2005, 6457–6474.CrossRefGoogle Scholar
  8. [8]
    Castanier, M.P. and Pierre, C., Lyapunov exponents and localization phenomena in multi-coupled nearly periodic systems, Journal of Sound and Vibration, Vol.183, 1995, 493–515.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Xie, W.C. and Ibrahim, A., Buckling mode localization in rib-stiffened plates with misplaced stiffeners — a finite strip approach, Chaos, Solitons and Fractals, Vol.11, 2000, 1543–1558.CrossRefGoogle Scholar
  10. [10]
    Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A., Determining Lyapunov exponents from a time series, Physica D, Vol.16, 1985, 285–317.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Cai, G.Q. and Lin, Y.K., Localization of wave propagation in disordered periodic structures, AIAA Journal, Vol.29, 1991, 450–456.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Qian, Z.H., Jin, F., Wang, Z.K. and Kishimoto, K., Dispersion relations for SH-wave propagation in periodic piezoelectric composite layered structures, International Journal of Engineering Science, Vol.42, 2004, 673–689.CrossRefGoogle Scholar
  13. [13]
    Chandra, H., Deymier, P.A. and Vasseur, J.O., Elastic wave propagation along waveguides in three-dimensional phononic crystals, Physical Review B, Vol.70, No.5, 2004, 1–6.CrossRefGoogle Scholar
  14. [14]
    Wang, G., Yu, D.L., Wen, J.H., Liu, Y.Z. and Wen, X.S., One-dimensional phononic crystals with locally resonant structures, Physics Letters A, Vol.327, 2004, 512–521.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Fengming Li
    • 1
  • Yuesheng Wang
    • 1
  • Ali Chen
    • 1
  1. 1.Institute of Engineering MechanicsBeijing Jiaotong UniversityBeijingChina

Personalised recommendations