Acta Mechanica Solida Sinica

, Volume 26, Issue 2, pp 177–188 | Cite as

Suppression of Bending Waves in a Periodic Beam with Timoshenko Beam Theory

Article

Abstract

Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy.

Key words

vibration control wave beam periodic structure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Huang, W.H., Wang, X.Q., Zhang, J.H. and Zheng, G.T., Some advances in the vibration control of aerospace flexible structures. Advances in Mechanics, 1997, 27(1): 5–18.MATHGoogle Scholar
  2. [2]
    Heckl, M.A., Investigation on the vibration of grillages and other simple beam structures. Journal of the Acoustical Society of America, 1964, 36: 1335–1343.CrossRefGoogle Scholar
  3. [3]
    Mead, D.J., Wave propagation and natural modes in periodic systems. Journal of Sound and Vibration, 1975, 40: 1–18.CrossRefGoogle Scholar
  4. [4]
    Mead, D.J., Wave propagation in continuous periodic structures: research contributions from Southampton. Journal of Sound and Vibration, 1996, 190: 495–524.CrossRefGoogle Scholar
  5. [5]
    Yeh, J.Y. and Chen, L.W., Wave propagations of a periodic sandwich beam by FEM and the transfer matrix method. Composite Structures, 2006, 73: 53–60.CrossRefGoogle Scholar
  6. [6]
    Brennan, M.J., Elliott, S.J. and Pinnington, R.J., Strategies for the active of flexural vibration on a beam. Journal of Sound and Vibration, 1995, 186: 657–688.CrossRefGoogle Scholar
  7. [7]
    Chen, T., Hu, C. and Huang, W.H., Vibration control of cantilevered Mindlin-type plates. Journal of Sound and Vibration, 2009, 320: 221–234.CrossRefGoogle Scholar
  8. [8]
    El-Khatib, H.M., Mace, B.R. and Brennan, M.J., Suppression of bending waves in a beam using a tuned vibration absorber. Journal of Sound and Vibration, 2005, 288: 1157–1175.CrossRefGoogle Scholar
  9. [9]
    Gardonio, P. and Elliott, S.J., Active control of waves on a one-dimensional structure with a scattering termination. Journal of Sound and Vibration, 1996, 192: 701–730.CrossRefGoogle Scholar
  10. [10]
    Mace, B.R., Active control of flexural vibrations. Journal of Sound and Vibration, 1987, 114: 253–270.CrossRefGoogle Scholar
  11. [11]
    Chen, S.H., Wang, Z.D. and Liu, X.H., Active vibration control and suppression for intelligent structures. Journal of Sound and Vibration, 1997, 200: 167–177.CrossRefGoogle Scholar
  12. [12]
    Mei, C., Mace, B.R. and Jones, R.W., Hybrid wave/mode active vibration control. Journal of Sound and Vibration, 2001, 247: 765–784.CrossRefGoogle Scholar
  13. [13]
    Hu, C., Chen, T. and Huang, W.H., Active vibration control of Timoshenko beam based on hybrid wave/mode method. Acta Aeronautica et Astronautica Sinica, 2007, 28: 301–308.Google Scholar
  14. [14]
    Elliott, S.J. and Billet, L., Adaptive control of flexural waves propagating in a beam. Journal of Sound and Vibration, 1993, 163: 295–310.CrossRefGoogle Scholar
  15. [15]
    Carvalho, M.O.M. and Zindeluk, M., Active control of waves in a Timoshenko beam. International Journal of Solids and Structures, 2001, 38: 1749–1764.CrossRefGoogle Scholar
  16. [16]
    Ruzzene, M. and Baz, A., Control of wave propagation in periodic composite rods using shape memory inserts. ASME Journal of Vibration and Acoustics, 2000, 122: 151–159.CrossRefGoogle Scholar
  17. [17]
    Xiang, H.J. and Shi, Z.F., Analysis of flexural vibration band gaps in periodic beams using differential quadrature method. Computers and Structures, 2009, 87: 1559–1566.CrossRefGoogle Scholar
  18. [18]
    Li, F.M., Wang, Y.SH., 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, 2005, 281(1–2): 261–273.CrossRefGoogle Scholar
  19. [19]
    Li, F.M., Wang, Y.S., Hu, C. and Huang, W.H., Localization of elastic waves in randomly disordered multi-coupled multi-span beams. Waves in Random Media, 2004, 14(3): 217–227.CrossRefGoogle Scholar
  20. [20]
    Wang, Y.Z., Li, F.M., Huang, W.H. and Wang, Y.S., The Propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals. Journal of the Mechanics and Physics of Solids, 2008, 56: 1578–1590.CrossRefGoogle Scholar
  21. [21]
    Wang, Y.Z., Li, F.M., Kishimoto, K., Wang, Y.S. and Huang, W.H., Wave localization in randomly disordered periodic piezoelectric rods with initial stress. Acta Mechanica Solida Sinica, 2008, 21: 529–535.CrossRefGoogle Scholar
  22. [22]
    Wang, Y.Z., Li, F.M., Kishimoto, K., Wang, Y.S. and Huang, W.H., Wave localization in randomly disordered layered three-component phononic crystals with thermal effects. Archive of Applied Mechanics, 2010, 80: 629–640.CrossRefGoogle Scholar
  23. [23]
    Baz, A., Active control of periodic structures. ASME Journal of Vibration and Acoustics, 2001, 123: 472–479.CrossRefGoogle Scholar
  24. [24]
    Thorp, O., Ruzzene, M. and Baz, A., Attenuation and location of wave propagation in rods with periodic shunted piezoelectric patches. Smart Materials and Structures, 2001, 10: 979–989.CrossRefGoogle Scholar
  25. [25]
    Gibbs, G.P. and Fuller, C.R., Excitation of thin beams using asymmetric piezoelectric actuators. Journal of the Acoustical Society of America, 1992, 92: 3221–3227.CrossRefGoogle Scholar
  26. [26]
    Wen, X.S., Phononic Crystals. Bei Jing: National Defense Industry Press, 2009.Google Scholar
  27. [27]
    Brillouin, L., Wave Propagation in Periodic Structures. New York: Dover, 1953.MATHGoogle Scholar
  28. [28]
    Achenbach, J.D., Wave Propagation in Elastic Solids. Elsevier Science, 1984.CrossRefGoogle Scholar
  29. [29]
    Hu, H.C., On the method of Lagrange multiplier and others. Acta Mechanica Sinica, 1985, 17(5): 426–434.MathSciNetMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.College of ScienceHarbin Engineering UniversityHarbinChina

Personalised recommendations