Skip to main content
Log in

Flexural vibration analysis of an eccentric annular Mindlin plate

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

A weak-form quadrature element method is presented to study the flexural vibrations of an eccentric annular Mindlin plate. Typical combinations of boundary conditions are considered and the natural frequencies are obtained for both thin and moderately thick plates. All results are verified using the commercial computer code ANSYS. Excellent agreement is reached in all cases. Comparison of the present predictions with other available results for thin plates is also made.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bert C.W., Malik M. (1996) Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49:1–27

    Article  Google Scholar 

  2. Davis, P.I., Rabinowitz, P.: Methods of Numerical Integration, 2nd edn. Academic, Orlando (1984)

  3. Gordon W.J. (1971) Blending function methods of bivariate and multivariate interpolation and approximation. SIAM J. Numer. Anal. 8:158–177

    Article  MathSciNet  MATH  Google Scholar 

  4. Khurasia H.B., Rawtani S. (1978) Vibration analysis of circular plates with eccentric hole. ASME J. Appl. Mech. 45:215–217

    Google Scholar 

  5. Lin W.H. (1982) Free transverse vibrations of uniform circular plates and membranes with eccentric holes. J. Sound Vib. 81(3):425–435

    Article  MATH  Google Scholar 

  6. Mindlin R.D. (1951) Influence of rotatory inertia and shear in flexural motion of isotropic elastic plates. J. Appl. Mech. 18(3):1031–1036

    Google Scholar 

  7. Nagaya K. (1977) Transverse vibration of a plate having an eccentric inner boundary. ASME J. Appl. Mech. 44:165–166

    Google Scholar 

  8. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes—The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)

  9. Quan J.R., Chang C.T. (1989) New insights in solving distributed system equations by the quadrature method—I. Anal. Comput. Chem. Eng. 13:779–788

    Article  Google Scholar 

  10. Shu C. (2000) Differential Quadrature and its Application in Engineering. Springer, London

    MATH  Google Scholar 

  11. Szabó B.A., Babuška I. (1991) Finite Element Analysis. Wiley, New York

    MATH  Google Scholar 

  12. Vogel S.M., Skinner D.W. (1965) Natural frequencies of transversely vibrating annular plates. ASME J. Appl. Mech. 32:926–931

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hongzhi Zhong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhong, H., Yu, T. Flexural vibration analysis of an eccentric annular Mindlin plate. Arch Appl Mech 77, 185–195 (2007). https://doi.org/10.1007/s00419-006-0083-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-006-0083-z

Keywords

Navigation