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Vibration of Rectangular Plates Point-Supported at the Corners

Published online by Cambridge University Press:  07 June 2016

Hugh L. Cox  and
Jack Boxer
Hugh L. Cox
Affiliation:
The Martin Company, Denver, Colorado
Jack Boxer
Affiliation:
The Martin Company, Denver, Colorado
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Summary

The fundamental frequencies of flexural vibration are determined for uniform isotropic rectangular plates that have free edges and pinpoint supports at the four corners. For the particular case of a square plate the lowest five frequencies and mode shapes have been determined. The second frequency is most unusual, since an infinite number of mode shapes exist with identical frequencies. Finite difference expressions, which simplify the treatment of the free boundaries for definite values of Poisson's ratio, are used in conjunction with extrapolation procedures to obtain the approximate solutions.

Type
Research Article
Information
Aeronautical Quarterly , Volume 11 , Issue 1 , February 1960 , pp. 41 - 50
Copyright
Copyright © Royal Aeronautical Society. 1960

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References

1. Jensen, V. P. Analysis of Skew Slabs. University of Illinois Engineering Experimental Station Bulletin No. 332, pp. 48–49, 1941.Google Scholar
2. Livesley, R. K. and Birchaix, P. C. Analysis of a Loaded Cantilever Plate by Finite Difference Methods. Royal Aircraft Establishment Technical Note M.S. 26, p. 15, June 1956.Google Scholar
3. Salvadori, M. G. Numerical Computation of Buckling Loads by Finite Differences. Transactions of the American Society of Civil Engineers, Vol. 116, pp. 590–624, 1951.CrossRefGoogle Scholar
4. Ritz, W. Theorie der Transversalschwingungen einer quadratischen Platten mit freien Randern. Annalen der Physik, Leipzig, Vol. 28, p. 737, 1909.Google Scholar
5. Waller, Mary D. Vibrations of Free Square Plates: Part 1—Normal Vibrating Modes. Proceedings of the London Physical Society, Vol. 51, p. 835 and p. 843, 1939.Google Scholar