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.
Similar content being viewed by others
References
Bert C.W., Malik M. (1996) Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49:1–27
Davis, P.I., Rabinowitz, P.: Methods of Numerical Integration, 2nd edn. Academic, Orlando (1984)
Gordon W.J. (1971) Blending function methods of bivariate and multivariate interpolation and approximation. SIAM J. Numer. Anal. 8:158–177
Khurasia H.B., Rawtani S. (1978) Vibration analysis of circular plates with eccentric hole. ASME J. Appl. Mech. 45:215–217
Lin W.H. (1982) Free transverse vibrations of uniform circular plates and membranes with eccentric holes. J. Sound Vib. 81(3):425–435
Mindlin R.D. (1951) Influence of rotatory inertia and shear in flexural motion of isotropic elastic plates. J. Appl. Mech. 18(3):1031–1036
Nagaya K. (1977) Transverse vibration of a plate having an eccentric inner boundary. ASME J. Appl. Mech. 44:165–166
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes—The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)
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
Shu C. (2000) Differential Quadrature and its Application in Engineering. Springer, London
Szabó B.A., Babuška I. (1991) Finite Element Analysis. Wiley, New York
Vogel S.M., Skinner D.W. (1965) Natural frequencies of transversely vibrating annular plates. ASME J. Appl. Mech. 32:926–931
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-006-0083-z