AXISYMMETRIC DYNAMIC BEHAVIOUR OF THIN OBLATE SHELLS

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Published: 2024-02-25
DOI: https://doi.org/10.31026/j.eng.2009.04.13

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Ahmed A. Al – Rajihy
Ala M. Hussein Al – Jessany
Nawal H. Al – Raheimy

Abstract

This paper presents a theoretical investigation of the axisymmetric free vibrations of an isotropic thin oblate spheroid shell. The analysis depends on the Rayliegh – Ritz's method. The non – shallow shell theory is used for the analysis. The analysis based on considering the oblate spheroid as a continuous system constructed from two spherical shell elements matched at the continuous boundaries.
Throughout the results, it is shown that when the eccentricity reaches zero, an exact thin sphere solution is emerged and when the eccentricity equals one an exact thin circular plate solution is emerged. Therefore, the eccentricity of an oblate shell at medium value lies between these two values.
It was found that the Rayleigh – Ritz's method is suitable for all eccentricities, while the literature showed that the Rayleigh's method is suitable for eccentricities less than 0.6.

Article Details

Issue

Vol. 15 No. 04 (2009): Journal of Engineering

Section

Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 
 

How to Cite

“AXISYMMETRIC DYNAMIC BEHAVIOUR OF THIN OBLATE SHELLS” (2024) Journal of Engineering, 15(04), pp. 4305–4320. doi:10.31026/j.eng.2009.04.13.

References

 Antoine Chaigne, Mathieu Fontaine, Oliver Thomas, Michel Ferre, Cyril Tou., "Vibrations of Shallow Spherical Shells and Gongs", J. of Sound and Vibration, 2002.

 Chang Y. C. and Demkowicz L., "A stability Analysis Vibrating Viscoelastic Spherical Shells", J. Appl. Math., Vol. 2(2), PP. 213 – 242, 1998.

 Fawaz Abbas Najim, "An Investigation into the Free axisymmetric vibration characteristics of isotropic thin oblate spheroidal shells", M. Sc. Thesis, Mechanical Engineering/ University of Baghdad, 1990.

 Haym Benaroya, "Mechanical Vibration", Prentice – Hill, Inc., U.S.A., 1998.

 Kalnins A., "Effect of bending on vibrations of spherical shells", J. Acoust. Soc. Amer., Vol.

 36 (1), PP. 74 – 81, 1964.

 Kraus H., "Thin elastic shells", John Wiley and Sons, New York 1967.

 Nawal H. A. , “ Theoretical Investigation of the Axisymmetric Free Vibration of An Oblate Spheroid Shells”, M. Sc. Thesis, Mechanical Engineering/ University of Babylon, 2005.

 Penzes L. and Burgin G.," Free vibrations of thin isotropic oblate spheroidal shells", General Dynamic Report No. GD/C–BTD 65 – 113, 1965

 Penzes L., " Free vibrations of thin orthotropic oblate spheroidal shells", J. Acoust. Soc. Amer., Vol. 45, pp. 500 – 505, 1969.

 Tavakoli M. S. and Singh R., "Eigensolutions of joined / hermetic shell structures using the state space method", J. Sound and Vibration Vol. 100, PP. 97 – 123, 1989.

 Wilfred E. Baker " Axisymmetric modes of vibration of thin spherical shell", J. Acoust. Soc. Amer., Vol. 33, PP. 1749 – 1758, 1961.