Bending of Sector Plates on Elastic Foundations by Bessel Functions
Publication: Journal of Engineering Mechanics
Volume 126, Issue 6
Abstract
A series solution approach based on the complex Bessel functions is presented in this paper for the analysis of bending of annual sector plates that are simply supported along their straight (or radial) edges, resting on Winkler-type elastic foundations. After a real general solution to a homogeneous differential equation of the bending plates is derived from the complex Bessel functions, the solution to the nonhomogeneous differential equation may be formulated by the general solution. Finally, some numerical examples are given to show the feasibility of this approach.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Cheung, M. S., and Chan, M. Y. T. (1981). “Static and dynamic analysis of thin and thick sector plates by the finite strip method.” Comp. and Struct., 33, 79–88.
2.
Harik, I. E. (1984). “Analytical solution to orthotropic sector.”J. Engrg. Mech., ASCE, 110(4), 554–568.
3.
Harik, I. E., and Motaghasemi, H. R. (1990). “Vibration of sector plates on elastic foundations.” J. Sound and Vibration, 138, 524–528.
4.
Hetenyi, M. (1946). Beam on elastic foundation. University of Michigan Press, Ann Arbor, Mich.
5.
Khyrasia, H. B., and Rawtani, S. (1979). “Vibration analysis of circular segment shaped plates.” J. Sound and Vibration, 67, 307–313.
6.
Leissa, A. W. (1978). “Recent studies in plate vibration.” The Shock and Vibration Digest, 19, 11–18.
7.
Onate, E., and Surez, B. (1983). “A unified approach for the analysis of bridges, plates and axisymmetrical shells using the linear Mindlin strip element.” Comp. and Struct., 17, 407–426.
8.
Panc, V. (1975). Theories of elastic plates. Noordhoff International, Leyden, The Netherlands.
9.
Reismann, H. (1954). “Bending of circular and ring-shaped plates on an elastic foundation.” J. Appl. Mech., 21, 45–51.
10.
Wilson, J. F., and Gary, D. P. (1978). “Frequencies of annular plate and curved beam element.” AIAA J., 16, 270–272.
11.
Yu, Y.-Y. (1957). “Axisymmetrical bending of circular plates under simultaneous action of lateral load, force in the middle plane, and elastic foundation.” J. Appl. Mech., 24, 141–143.
12.
Zhou, Y. H., Zheng, X. J., and Harik, I. E. (1995). “Semi-numerical method for buckling of sector plate.” Comp. and Struct., 57, 847–854.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 6 • June 2000
Pages: 653 - 655
History
Received: Apr 28, 1999
Published online: Jun 1, 2000
Published in print: Jun 2000
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.