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Bending of Elastically Restrained Rectangular Plates Under Uniform Pressure

Published online by Cambridge University Press:  04 July 2016

C. Lakshmi Kantham
C. Lakshmi Kantham*
Affiliation:
(Department of Aeronautical Engineering, Indian Institute of Science, Bangalore)
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Extract

In the bending and vibration of plates it is found that the values of maximum deflection and natural frequencies, respectively, vary considerably from the simply-supported to clamped edge conditions. For an estimation of these characteristics in the intermediate range a generalised boundary condition may be assumed, of which the simply-supported and clamped edges become limiting cases. While Bassali considers the ratio of edge moment to the cross-wise moment as a constant, Newmark, Lurie and Klein and other investigators, in their analyses of various structures, consider that moment and slope at an end are proportional.

Here the definition of elastic restraint as given by Timoshenko, α=βM, is followed, where α is the slope at any edge, M the corresponding edge moment per unit length while β is the elastic restraint factor. β→0 and β→∞ represent the two limiting cases of simply-supported and clamped edge conditions.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 62 , Issue 575 , November 1958 , pp. 834 - 836
Copyright
Copyright © Royal Aeronautical Society 1958

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References

1.Bassali, W. A. (1956). Bending of an Elastically Restrained Circular Plate under a Linearly Varying Load over an Eccentric Circle. Proceedings of Cambridge Philosophical Society, Vol. 52, pp. 134–141, October 1956.Google Scholar
2.Newmark, N. M. (1949). A Simple Approximate Formula for Effective End Fixity of Columns. Journal of the Aeronautical Sciences, Vol. 16, p. 116, February 1949.Google Scholar
3.Lurie, H. (1951). Effective End Restraints of Columns by Frequency Measurements. Journal of the Aeronautical Sciences, Vol. 18, pp. 566–567, August 1951.CrossRefGoogle Scholar
4.Klein, B. (1957). Determination of Effective End Fixity of Columns with Unequal Rotational End Restraints by Means of Vibration Test Data. Journal of the Royal Aeronautical Society, Vol. 61, p. 131, February 1957.Google Scholar
5.Winter, G., Hsu, P.T., Koo, B., and Loh, M. H. (1948). Buckling of Trusses and Rigid Frames. Cornell University Engineering Experimental Station Bulletin No. 36, pp. 1-63, April 1948.Google Scholar
6.Joga Rao, C. V., and Lakshmi Kantham, C. (1957). Natural Frequencies of Rectangular Plates with Edges Elastically Restrained against Rotation. Journal of the Aeronautical Sciences, Vol. 24, pp. 855–856, November 1957.Google Scholar
7.Timoshenko, S. P. (1940). Theory of Plates and Shells. McGraw-Hill Book Co. Inc., New York, p. 17, 1940.Google Scholar
8.Timoshenko, S. P. (1940). Theory of Plates and Shells. McGraw-Hill Book Co. Inc., New York, pp. 222–228, 1940.Google Scholar