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A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

Published online by Cambridge University Press:  04 July 2016

C. L. Kirk
C. L. Kirk*
Affiliation:
The Post Graduate Department of Applied Mechanics, The University of Sheffield
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Extract

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 66 , Issue 616 , April 1962 , pp. 240 - 241
Copyright
Copyright © Royal Aeronautical Society 1962

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References

1.Cox, H. L. and Boxer, J. (1960). Vibration of Rectangular Plates Point-Supported at the Corners, Aeronautical Quarterly, Vol. 11, Part 1, pp. 41–50, February 1960.Google Scholar
2.Timoshenko, S. (1955). Vibration Problems in Engineering, D. Van Nostrand Company Inc., New York, N.Y.3rd Edition, p. 442, 1955.Google Scholar
3.LordRayleigh, . Theory of Sound, Vol. 1, 2nd Edition, p. 109 et seq., MacMillan and Company Limited, London.Google Scholar