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Acta Mechanica Solida Sinica

, Volume 23, Issue 5, pp 377–385 | Cite as

Active Vibration Control of Finite L-Shaped Beam with Travelling Wave Approach

  • Chunchuan Liu
  • Fengming Li
  • Wenhu Huang
Article

Abstract

In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam are studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite L-shaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.

Key words

finite L-shaped beam active vibration control travelling wave approach power flow 

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References

  1. [1]
    Yan, J., Li, T.Y., Liu, J.X. and Zhu, X., Input power flow in a submerged infinite cylindrical shell with doubly periodic supports. Applied Acoustics, 2008, 69: 681–690.CrossRefGoogle Scholar
  2. [2]
    Massonb, P. and Berry, A., Investigation of active structural intensity control in finite beams: Theory and experiment. The Journal of the Acoustical Society of America, 2000, 108(2): 612–623.CrossRefGoogle Scholar
  3. [3]
    Park, Y.H. and Hong, S.Y., Vibrational power flow models for transversely vibrating finite Mindlin plate. Journal of Sound and Vibration, 2008, 317: 800–840.CrossRefGoogle Scholar
  4. [4]
    Choi, W.J., Xiong, Y.P. and Shenoi, R.A., Power flow analysis for a floating sandwich raft isolation system using a higher-order theory. Journal of Sound and Vibration, 2009, 319: 228–246.CrossRefGoogle Scholar
  5. [5]
    Lyon, R.H., Statistical Energy Analysis. Cambridge, Massachusetts: MIT Press, 1975.Google Scholar
  6. [6]
    Mace, B.R., Power flow between two continuous one-dimension subsystems: A wave solution. Journal of Sound and Vibration, 1992, 154(2): 289–319.CrossRefGoogle Scholar
  7. [7]
    Mace, B.R., The statistics of power flow between two continuous one dimension subsystems. Journal of Sound and Vibration, 1992, 154(2): 321–341.CrossRefGoogle Scholar
  8. [8]
    Romanoa, A.J., Abraham, P.B. and Williams, E.G., A Poynting vector formulation for thin shells and plates, and its application to structural intensity analysis and source localization. Part I: Theory. The Journal of the Acoustical Society of America, 1990, 87(3): 1166–1175.CrossRefGoogle Scholar
  9. [9]
    McCollum, M.D. and Cuschieri, J.M., Bending and in-plane wave transmission in thick connected plates using statistical energy analysis. The Journal of the Acoustical Society of America, 1990, 88(3): 1480–1485.CrossRefGoogle Scholar
  10. [10]
    Cuschieri, J.M., Structural power-flow analysis using a mobility approach of an L-shaped plate. The Journal of the Acoustical Society of America, 1990, 87(3): 1159–1165.CrossRefGoogle Scholar
  11. [11]
    Kessissoglou, N.J., Power transmission in L-shaped plates including flexural and in-plane vibration. The Journal of the Acoustical Society of America, 2004, 115(3): 1157–1169.CrossRefGoogle Scholar
  12. [12]
    Pan, X. and Hansen, C.H., Active control of vibratory power transmission along a semi-infinite plate. Journal of Sound and Vibration, 1995, 184(4): 585–610.CrossRefGoogle Scholar
  13. [13]
    Hansen, C.H. and Pan, X., The effect of error sensor location and type on the active control of beam vibration. Journal of Sound and Vibration, 1993, 165(3): 497–510.CrossRefGoogle Scholar
  14. [14]
    Cheng, W. and Wang, D.J., Active control of flexible beams subjected to multi-disturbance using one controller. Acta Mechanica Sinica, 1997, 13(3): 273–279.CrossRefGoogle Scholar
  15. [15]
    Ming, R.S., The estimate and measurement of longitudinal wave intensity. Acta Mechanica Sinica, 1996, 12(3): 251–262.CrossRefGoogle Scholar
  16. [16]
    Zhu, H.P. and Tang, J.X., The power-flow and traveling-wave approach to the vibration analysis of base-isolated multistory buildings. Acta Mechanica Solida Sinica, 1995, 8(3): 228–235.MathSciNetGoogle Scholar
  17. [17]
    Halkyard, C.R. and Mace, B.R., Adaptive active control of flexural waves in a beam in the presence of a near field. Journal of Sound and Vibration, 2005, 285: 149–171.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Halkyard, C.R. and Mace, B.R., Feed-forward adaptive control of flexural vibration in a beam using wave amplitudes. Journal of Sound and Vibration, 2002, 254(1): 117–141.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Pao, Y.H., Su, X.Y. and Tian, J.Y., Reverberation method for propagation of sound in multilayered liquid. Journal of Sound and Vibration, 2000, 230(4): 743–760.CrossRefGoogle Scholar
  20. [20]
    Pao, Y.H., Chen, W.Q. and Su, X.Y., The reverberation-ray matrix and transfer matrix analyses of unidirectional wave motion. Wave Motion, 2007, 44: 419–438.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Guo, Y.Q. and Chen, W.Q., Dynamic analysis of space structures with multiple tuned mass damper. Engineering Structures, 2007, 27(12): 3390–3403.CrossRefGoogle Scholar
  22. [22]
    Guo, Y.Q., Chen, W.Q. and Pao, Y.H., Dynamic analysis of space frame: the method of reverberation-ray matrix and orthogonality of normal modes. Journal of Sound and Vibration, 2008, 317(3–5): 716–738.CrossRefGoogle Scholar
  23. [23]
    Cremer, L., Heckl, M. and Petersson, B.A.T., Structure-Borne Sound, third ed. Springer, Berlin, 2005.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina

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