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Effects of mixed elastic rotational edge restraints on the vibration, buckling and bending of circular plates

Published online by Cambridge University Press:  04 July 2016

David J. Gunaratnam  and
A. P. Bhattacharya
David J. Gunaratnam
Affiliation:
Department of Civil Engineering, University of the West Indies, St Augustine, Trinidad, (WI)
A. P. Bhattacharya
Affiliation:
Department of Mechanical Engineering, University of the West Indies, St Augustine, Trinidad, (WI)
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Summary

A general formulation based on a variational approach is used to study the static bending, vibration and stability of circular plates having mixed elastic rotational constraints at the boundary. A single displacement function suitable for these three classes of problems is used in a Ritz scheme to obtain static bending solutions and eigenvalues for various combinations of boundary parameters that exhibit symmetry about two axes. Results obtained are generally in good agreement with those available in the literature and in some cases represent an improvement on those previously reported. The lowest eigenvalues for the stability problem are presented for the first time.

Type
Research Article
Information
The Aeronautical Journal , Volume 89 , Issue 887 , September 1985 , pp. 257 - 262
Copyright
Copyright © Royal Aeronautical Society 1985 

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References

1. Nowacki, W. and Olesiak, Z. Vibration, buckling and bending of a circular plate clamped along part of its periphery and simply supported on the remaining part. Bulletin de l’Academie Polonaise des Sciences, 1956,4,247–258.Google Scholar
2. Bartlett, C. The vibration and buckling of a circular plate clamped on part of its boundary and simply supported on the remainder. Quarterly Journal of Mechanics and Applied Mathematics, 1963,16,431–440.Google Scholar
3. Noble, B. The vibration and buckling of a circular plate clamped on part of its boundary and simply supported on the remainder. Proceedings of the 9th Mid-western Mechanics Conference, University of Wisconsin, Madison, Wisconsin, August 1965,141–146.Google Scholar
4. Chen, S. S. H. and Pickett, G. Bending of uniform plates of arbitrary shapes and with mixed boundary conditions. Proceedings of the 10th Mid-western Mechanics Conference, Colorado State University, Fort Collins, Colorado, August 1967, 411–427.Google Scholar
5. Conway, H. D. and Farnham, K. A. Deflections of uniformly loaded circular plates with combinations of clamped, simply supported and free boundary conditions. International Journal of Mechanical Sciences. 1967,9,661–671.Google Scholar
6. Leissa, A. W. and Clausen, W. E. Deflections of a circular plate having mixed boundary conditions. Journal of the American Institute of Aeronautics and Astronautics, December 1967,5,2287.Google Scholar
7. Stahl, B. and Keer, L. M. Bending of a Uniformly loaded circular plate with mixed boundary conditions. Journal of the American Institute of Aeronautics and Astronautics, June 1972, 10,739–743.Google Scholar
8. Hirano, Y. and Okazaki, K. Vibrations of circular plates having partly clamped or partly simply supported boundary. Bulletin of the Japan Society of Mechanical Engineers, June 1976, 19,610–618.Google Scholar
9. Narita, Y. and Leissa, A. W. Transverse vibration of simply supported circular plates having partial elastic constraints. Journal of Sound and Vibration, 1980,70(1), 103–116.Google Scholar
10. Narita, Y. and Leissa, A. W. Flexural vibrations of free circular plates elastically constrained along parts of the edge. International Journal of Solids and Structures, 1981,17,83–92.Google Scholar
11. Eastep, F. E. and Hemming, F. G. Natural frequencies of circular plates with partially free, partially clamped edges. Journal of Sound and Vibration, 1982,84(3), 359–370.Google Scholar
12. Leissa, A. W. and Narita, Y. Natural frequencies of simply supported circular plates. Journal of Sound and Vibration, 1980, 70(2), 221–229.Google Scholar
13. Leissa, A. W., Laura, P. A. A. and Gutierrez, R. H. Transverse vibrations of circular plates having non-uniform edge constraints. Journal of the Acoustical Society of America, 1979, 66(1), 180–184.Google Scholar
14. Laura, P. A. A., Paloto, J. C. and Santos, R. D. A note on the vibration and stability of a circular plate elastically restrained against rotation. Journal of Sound and Vibration, 1975, 41(2), 177–180.Google Scholar
15. Laura, P. A. A. and Gelos, R. Further results on the vibration and stability of a circular plate elastically restrained against rotation. Journal of Sound and Vibration, 1975,41(3), 388–390.Google Scholar
16. Laura, P. A. A., Luisoni, L. E. and Lopoz, J. J. A note on free and forced vibrations of circular plates: the effect of support flexibility. Journal of Sound and Vibration, 1976,47(2), 287–291.Google Scholar
17. Grossi, R. O. and Laura, P. A. A. Transverse vibrations of circular plates of linearly varying thicknesses. Applied Acoustics, 1980,13,7–18.Google Scholar
18. Laura, P. A. A. and Ficcadenti, G. M. Transverse vibrations of circular plates of varying thickness with non-uniform edge constraints. Applied Acoustics, 1980,13,227–236.Google Scholar
19. Laura, P. A. A., Pardoen, G. C, Luisoni, L. E. and Avalos, D. Transverse vibrations of axisymmetric polar orthotropic circularplates elastically restrained against rotation along the edges. Fibre Science and Technology, 1981,15,65–77.Google Scholar
20. Laura, P. A. A. and Ficcadenti, G. M. Transverse vibrations and elastic stability of circular plates of variable thickness and with non-uniform boundary conditions. Journal of Sound and Vibration, 1981,77(3), 303–310.Google Scholar
21. Kantham, C. L. Bending and vibration of elastically restrained circular plates, Journal of the Franklin Institute, 1958, 265, 483–491.Google Scholar
22. Timoshenko, S. and Gere, J. M. Theory of Elastic Stability, McGraw-Hill, 1961.Google Scholar