This paper presents a method to analyze the free and forced vibration responses of a finite uniform cylindrical shell. The cross section of the shell is a square with rounded corners. This geometry makes the analysis of the system difficult. The approach in this work is to apply a conformal mapping to map the physical domain onto a circular cylindrical domain. The Rayleigh-Ritz method is applied to solve for the solution. Numerical results of the mode shapes and the forced response at different frequencies are presented.
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References
1.
1. J. L. Sewall and C. G. Pusey. Vibration study of clamped-free elliptical cylindrical shells. AIAA Journal, 9:1004-1011, 1971.
2.
2. K. Shirakawa and M. Morita. Vibration and buckling of cylinders with elliptical cross-section. Journal of Sound and Vibration, 84:121-131, 1982.
3.
3. B. I. Slepov. Vibrations and stability of anisotropic and sandwich cylindrical shells of arbitrary cross section. In Proceedings of the 4th All-Union Conference on Shells and Plates, pp. 826-834, 1962.
4.
4. L. D. Culberson and D. E. Boyd. Free vibrations of freely supported oval cylinders. AIAA Journal, 9(8):1474-1480, 1971.
5.
5. Y. N. Chen and J. Kempner. Modal method for free vibration of oval cylindrical shells with simply supported and clamped ends. Journal of Applied Mechanics,45:142-148, 1978.
6.
6. V. K. Koumousis and A. E. Armenakas. Free vibrations of simply supported cylindrical shells of oval cross-section. AIAA Journal, 21:1017-1027, 1983.
7.
7. K. P. Soldatos and G. J. Tzivanidis. Buckling and vibration of cross-ply laminated non-circular cylindrical shells. Journal of Sound and Vibration, 82:425-434, 1982.
8.
8. K. P. Soldatos. Equivalence of some methods used for the dynamic analysis of cross-ply laminated oval cylindrical shells. Journal of Sound and Vibration, 91:461-465, 1983.
9.
9. K. Suzuki, G. Shikanai and A. W. Leissa. Free vibrations of laminated composite non-circular thick cylindrical shells. International Journal of Solids and Structures, 33(27):4079-4100, 1996.
10.
10. R. M. Bergman. Investigation of the free vibrations of noncircular cylindrical shells. Journal of Applied Mathematics and Mechanics, 37:1068-1077, 1973.
11.
11. G. F. Elsbernd and A. W. Leissa. The vibrations of non-circular cylindrical shells with initial stresses. Journal of Sound and Vibration, 29:309-329, 1973.
12.
12. K. Suzuki, S. Tamura and T. Kosawada. Vibrations of noncircular cylindrical shells. Bulletin of the Japanese Society of Mechanical Engineers, 26(215):818-826, 1983.
13.
13. A. Kayran and J. R. Vinson. Torsional vibrations of layered composite paraboloidal shells. Journal of Sound and Vibration, 141(2):231-244, 1990.
14.
14. A. Kayran and J. R. Vinson. Effect of transverse shear deformation on the natural frequencies of layered composite paraboloidal shells. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 112(4):429-439, 1990.
15.
15. A. Kayran and J. R. Vinson. Free vibration analysis of laminated composite truncated circular conical shells. AIAA Journal, 28(7):1259-1269, 1990.
16.
16. A. C. Stevenson. The boundary couples in thin plates. Philosophical Magazine, 34:105-114, 1943.
17.
17. N. I. Muskhelishvili. Some Basic Problems of the Mathematical Theory of Elasticity. P. Noordhoff Ltd., Groningen, Holland, 1953.
18.
18. E. H. Mansfield. The Bending and Stretching of Plates. Pergamon Press, Oxford, 1964.
19.
19. M. M. Banerjee. Note on the large deflections of irregular shaped plates by the method of conformal mapping. Journal of Applied Mechanics, 43E(2):356-357, 1976.
20.
20. T. Irie, G. Yamada and M. Sonoda. Natural frequencies of square membrane and square plate with rounded corners. Journal of Sound and Vibration, 86(3):442-448, 1983.
21.
21. G. Yamada, T. Irie and Y. Tagawa. Free vibration of non-circular cylindrical shells with variable circumferential profile. Journal of Sound and Vibration, 95:117-126, 1984.
22.
22. J. R. Vinson and K. Potty. Behavior of composite material sandwich rings and shells sections in complex structures. In Proceedings of the Third International Conference on Sandwich Constructions, Southampton, 1995.
23.
23. K. P. K. Potty and J. R. Vinson. Circumferential and radial behavior of anisotropic shells of variable cross section. In Proceedings of the 11th Technical Conference of the American Society for Composites, Atlanta, Georgia, 1996.
24.
24. Z. Chen and J. R. Vinson. Bending stress reduction through mid-plane asymmetry in composite structures. In Proceedings of ASME AD—Recent Advances in Mechanics of Aerospace Structures and Materials, Vol. 56, pp. 187-192, 1998.
25.
25. J. M. M. Hernandez. Advances in Acoustics Technology. John Wiley and Sons. New York, 1995.
26.
26. A. W. Leissa. Vibration of Shells, NASA, Washington, D.C., 1973.
27.
27. V. V. Novozhilov. Foundations of the Nonlinear Theory of Elasticity. Graylock Press, Rochester, New York, U.S.A., 1953.
28.
28. J. R. Vinson and R. L. Sierakowski. The Behavior of Structures Composed of Composite Materials. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1987.
29.
29. J. R. Vinson. The Behavior of Shells Composed of Isotropic and Composite Materials, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
30.
30. L. Meirovitch. Analytical Methods in Vibrations. Macmillan, New York, 1967.
