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Compounded Normal Modes of Free Vibration of Cantilever Plates

Published online by Cambridge University Press:  04 July 2016

C. L. Kirk
C. L. Kirk*
Affiliation:
Department of Aircraft Design, College of Aeronautics, Cranfield
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Extract

In the vibration of isotropic rectangular plates, the phenomenon of the simultaneous excitation of two separate modes having equal frequencies is well known. Wallerobserved complex nodal patterns on isotropic rectangular plates, and she stated that such combinations were possible because of the internal damping of the plates, which reduced the sharpness of resonance.

Warburton considered the existence of modes m/n±n/m for a clamped plate and showed that when a plate is square, for the mode 4/2 + 2/4, the nodal lines do not lie parallel to the edges of the plate. Furthermore, it was proved that for a square clamped plate, the modes m/n±n/m have discrete frequencies.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 71 , Issue 680 , August 1967 , pp. 584 - 585
Copyright
Copyright © Royal Aeronautical Society 1967

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References

1.Waller, M. D.Vibration of Free Square Plates. Part II Compounded Normal Modes. Proceedings of the Physical Society of London, Vol. 452, p 452, 1940.Google Scholar
2.Warburton, G. B.The Vibration of Rectangular Plates. Proceedings of the IMechE (London), Vol. 168, No. 12, 1954.Google Scholar
3.Hoppmann, W. H. and Magness, L. S.Nodal Patterns of the Free Flexural Vibration of Stiffened Plates. Journal of Applied Mechanics, Vol. 24, pp 526–530, 1957.CrossRefGoogle Scholar
4.Kirk, C. L.Vibration Characteristics of Stiffened Plates. PhD Thesis, Sheffield University, 1959.Google Scholar
5.Bishop, R. E. D. and Johnson, D. C.The Mechanics of Vibration. Cambridge University Press, 1960.Google Scholar