Skip to main content
SpringerLink
Log in

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach. The dynamic responses, active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT). To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate, the near-field and far-field waves are entirely contained in the wave approach. The in-plane longitudinal and shear waves are also considered. The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies. The influence of the plate thickness on the vibrational power flow is investigated. From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies. Furthermore, the effects of structural damping on the active and reactive power flow at the junction are also analyzed.

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. Kessissoglou, N.J.: Active attenuation of the wave transmission through an L-plate junction. J. Acoust. Soc. Am. 110(1), 267–277 (2001)

    Article  Google Scholar 

  2. Kessissoglou, N.J.: An analytical and experimental investigation on active control of the flexural wave transmission in a simply supported bibbed plate. J. Sound Vib. 240(1), 73–85 (2001)

    Article  Google Scholar 

  3. Keir, J., Kessissoglou, N.J., Norwood, C.: An analytical investigation of single actuator and error sensor control in connected plates. J. Sound Vib. 271(2), 635–649 (2004)

    Article  Google Scholar 

  4. Kessissoglou, N.J.: Power transmission in L-shaped plates including flexural and in-plane vibration. J. Acoust. Soc. Am. 115(3), 1157–1169 (2004)

    Article  Google Scholar 

  5. Keir, J., Kessissoglou, N.J., Norwood, C.J.: Active control of connected plates using single and multiple actuators and error sensors. J. Sound Vib. 281(1), 73–97 (2005)

    Article  Google Scholar 

  6. Mindlin, R.D.: Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. 18(1), 31–38 (1951)

    MATH  Google Scholar 

  7. Mindlin, R.D., Schachow, A., Deresiewicz, H.: Flexural vibrations of rectangular plate. J. Appl. Mech. 23(3), 430–436 (1956)

    MATH  Google Scholar 

  8. Dawe, D.J., Roufaeil, O.L.: Rayleigh-Ritz vibration analysis of Mindlin plates. J. Sound Vib. 69(3), 345–359 (1980)

    Article  MATH  Google Scholar 

  9. Liew, K.M., Hung, K.C., Lim, M.K.: Vibration of Mindlin plates using boundary characteristic orthogonal polynomials. J. Sound Vib. 182(1), 77–90 (1995)

    Article  Google Scholar 

  10. Lee, J.M., Kim, K.C.: Vibration analysis of rectangular isotropic thick plate using Mindlin plate characteristic functions. J. Sound Vib. 187(5), 865–877 (1995)

    Article  Google Scholar 

  11. Liu, F.L., Liew, K.M.: Free vibration analysis of Mindlin sector plates: numerical solutions by differential quadrature method. Comput. Method Appl. M. 177(1–2), 77–92 (1999)

    Article  MATH  Google Scholar 

  12. Xiang, Y., Liew, K.M., Kitipornchai, S.: Vibration analysis of rectangular Mindlin plates resting on elastic edge supports. J. Sound Vib. 204(1), 1–16 (1997)

    Article  Google Scholar 

  13. Xiang, Y., Zhang, L.: Free vibration analysis of stepped circular Mindlin plates. J. Sound Vib. 280(3–5), 633–655 (2005)

    Article  Google Scholar 

  14. Zhou, D.: Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method. Int. J. Solids Struct. 38(32–33): 5565–5580 (2001)

    Article  MATH  Google Scholar 

  15. Zhou, D., Lo, S.H., Au, F.T.K., et al.: Vibration analysis of rectangular Mindlin plates with internal line supports using static Timoshenko beam functions. Int. J. Mech. Sci. 44(12), 2503–2522 (2002)

    Article  MATH  Google Scholar 

  16. Labuschagne, A., Rensburg, N.F.J., Merwe, A.J.: Vibration of a Reissner-Mindlin-Timoshenko plate-beam system. Math. Comput. Model 50(7–8), 1033–1044 (2009)

    Article  MATH  Google Scholar 

  17. Hashemi, S.H., Omidi, M., Taher, H.R.D.: The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plates on the elastic foundation. Eur. J. Mech. A-Solid 28(2), 289–304 (2009)

    Article  MATH  Google Scholar 

  18. Akhavan, H., Hashemi, S.H., Taher, H.R.D., et al.: Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis. Comp. Mater. Sci. 44(3), 951–961 (2009)

    Article  Google Scholar 

  19. Hashemi, S.H., Khorshidi, K., Taher, H.R.D.: Exact acoustical analysis of vibrating rectangular plates with two opposite edges simply supported via Mindlin plate theory. J. Sound Vib. 322(4–5), 883–900 (2009)

    Article  Google Scholar 

  20. Xiang, Y., Lai, S.K., Zhou, L.: DSC-element method for free vibration analysis of rectangular Mindlin plates. Int. J. Mech. Sci. 52(4), 548–560 (2010)

    Article  Google Scholar 

  21. Shen, H.S., Yang, J., Zhang, L.: Dynamic response of Reissner-Mindlin plates under thermomechanical loading and resting on elastic foundations. J. Sound Vib. 232(2), 309–329 (2000)

    Article  Google Scholar 

  22. Yu, L., Shen, H.S., Hu, X.P.: Dynamic responses of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations. J. Sound Vib. 299(1-2), 212–228 (2007)

    Article  Google Scholar 

  23. Pan, X., Hansen, C.H.: The effect of error sensor location and type on the active control of beam vibration. J. Sound Vib. 165(3), 497–510 (1993)

    Article  MATH  Google Scholar 

  24. Pan, X., Hansen, C.H.: Active control of vibratory power transmission along a semi-infinite plate. J. Sound Vib. 184(4), 585–610 (1995)

    Article  MATH  Google Scholar 

  25. Mace, B.R.: Power flow between two continuous one-dimension subsystems: A wave solution. J. Sound Vib. 154(2), 289–319 (1992)

    Article  MATH  Google Scholar 

  26. Mace, B.R.: The statistics of power flow between two continuous one dimension subsystems. J. Sound Vib. 154(2), 321–341 (1992)

    Article  MATH  Google Scholar 

  27. McCollum, M.D., Cuschieri, J.M.: Bending and in-plane wave transmission in thick connected plates using statistical energy analysis. J. Acoust. Soc. Am. 88(3), 1480–1485 (1990)

    Article  Google Scholar 

  28. Cuschieri, J.M.: Structural power-flow analysis using a mobility approach of an L-shaped plate. J. Acoust. Soc. Am. 87(3),1159–1165 (1990)

    Article  Google Scholar 

  29. Cuschieri, J.M.: Parametric analysis of the power flow on an Lshaped plate using a mobility power flow approach. J. Acoust. Soc. Am. 91(5), 2686–2695 (1992)

    Article  Google Scholar 

  30. McCollum, M.D.: Vibrational power flow in thick connected plates. [Ph.D. Thesis], Florida Atlantic University Boca Raton (1988)

  31. Cuschieri, J.M., McCollum, M.D.: Thick plate bending wave transmission using a mobility power flow approach. J. Acoust. Soc. Am. 88(3), 1472–1479 (1990)

    Article  Google Scholar 

  32. Cuschieri, J.M., McCollum, M.D.: In-plane and out-of-plane waves’ power transmission through a L-plate junction using the mobility power flow approach. J. Acoust. Soc. Am. 100(2), 857–870 (1996)

    Article  Google Scholar 

  33. Park, Y.H., Hong, S.Y.: Vibrational power flow models for transversely vibrating finite Mindlin plate. J. Sound Vib. 317(3–5), 800–840 (2008)

    Article  Google Scholar 

  34. Liu, C.C., Li, F.M., Fang, B., et al.: Active control of power flow transmission in finite connected plate. J. Sound Vib. 329(20), 4124–4135 (2010)

    Article  Google Scholar 

  35. Hu, C., Han, G., Li, F.M., et al.: Scattering of flexural waves and boundary-value problem in Mindlin’s plates of soft ferromagnetic material with a cutout. J. Sound Vib. 312(1–2), 151–165 (2008)

    Article  Google Scholar 

  36. Bercin, A.N., Langley, R.S.: Application of the dynamic stiffness technique to the in-plane vibrations of plate structures. Comput. Struct. 59(5), 869–875 (1996)

    Article  MATH  Google Scholar 

  37. Pao, Y.H., Mow, C.C.: Diffraction of elastic waves and dynamic stress concentrations. Crane, Russak & Company Inc US (1973)

Download references

Author information

Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, P. O. Box 137, 150001, Harbin, China

    Chun-Chuan Liu, Feng-Ming Li, Ting-Wei Liang & Wen-Hu Huang

Authors
  1. Chun-Chuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng-Ming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ting-Wei Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wen-Hu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng-Ming Li.

Additional information

The project was supported by the National Basic Research Program of China (2011CB711102) and the National Natural Science Foundation of China (10672017, 11002045).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, CC., Li, FM., Liang, TW. et al. The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges. Acta Mech Sin 27, 785–795 (2011). https://doi.org/10.1007/s10409-011-0477-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-011-0477-1

Keywords

Search

Navigation