Abstract
In this vibration analysis, influence of ring supports on functionally gradient threelayered sandwich cylindrical shells is presented with middle layer fabricated of isotropic material. The ring support is introduced beside radial direction of the shell. Love’s first order thin shell theory is used for strain- and curvature-displacements relationship. Rayleigh–Ritz approach is employed to form the shell frequency equation. Axial modal dependence is approximated by characteristics beam functions. Study is carried out for placing ring support in different position of the shell, for different configuration of the functionally graded material’s layers to investigate the natural frequencies of the cylindrical shells under different boundary conditions for a number of physical parameters. Results obtained are validated with the previous published works in the open literature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arshad, S.H., Naeem, M.N., Sultana, N., Shah, A.G., & Iqbal, Z. 2010. Vibration of bilayered cylindrical shells with layers of different materials. J. Mech. Sci. Technol 24(3), :805–810.
Arshad, S. H., Naeem, M. N., Sultana, N., Iqbal, Z., & Shah, A.G. 2011. Vibration analysis of bilayered FGM cylindrical shells, Arch. Appl. Mech. 81(3): 319–343.
Isvandzibaei. M. R. & Awasare. P. J. 2010. Effects edge and free-free boundary conditions for analysis, free vibration of functionally graded cylindrical shell with ring based on third order shear deformation theory using Hamilton’s Principle. World Academy of Science, Engineering and Technology 61: 219–225.
Li, S., Fu, X. & Batra, R. C. 2010. Free vibration of three-layer circular cylindrical shells with functionally graded middle layer. Mechanics Research Communications 37: 577–580.
Love, A.E.H. 1888. On the small free vibrations and deformations of thin elastic shells. Phil. Trans. Royal Society of London 179 A: 125–137.
Loy, C. T. & Lam, K. Y. 1997. Vibration of cylindrical shells with ring support. Int. J. Mech. Sci. 39 (4): 455–471.
Loy, C. T., Lam, K.Y. & Reddy, J. N. 1999. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences 41: 309–324.
Naeem, M. N., Arshad, S. H. & Sharma, C. B., 2009. The Ritz formulation applied to the study of vibration frequency characteristics of functionally graded circular cylindrical shells, Journal of Mechanical Engineering Science, Part C 224: 43–53.
Najafizadeh, M. M. & Isvandzibaei, M. R. 2007. Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mechanica 191: 75–91.
Pradhan, S. C., Loy, C. T., Lam, K.Y. & Reddy, J. N. 2000. Vibration Characteristics of Functionally Graded Cylindrical Shells under Various Boundary Conditions. Applied Acoustics 61: 111–129.
Rayleigh, J.W.S. 1882. Theory of sound. 1: Macmillan, London.
Sewall, J.L. & Naumann, E.C. 1968. An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners. Langley research center, Langley station, Hampton, Va. NASA TN – 4705
Sharma, C. B. & Johns, D. J. 1971. Vibration characteristics of a clamped-free and clamped-ringstiffened circular cylindrical shell. Journal of Sound and Vibration 14 (4): 459–474.
Wang, C. M., Swaddiwudhipong, S. & Tian. J. 1997. Ritz method for vibration analysis of cylindrical shells with ring stiffeners. J. Engrg, Mech. 123 (2): 134–142.
Weingarten V. I. 1964. Free vibration of thin cylindrical shells. Northrop Corporation, Hawthorne, Calif, AIAA Journal 2 (4): 717–722.
Xiang, Y., Ma, Y. F., Kitipornchal, S., Lim, C. W. & Lau, C. W. H. 2002. Exact solutions for vibration of cylindrical shells with intermediate ring supports. International Journal of Mechanical Sciences 44: 1907–1924.
Xiang, Y., Wang, C. M., Lim, C. W. & Kitipornchai, S. 2005. Buckling of intermediate ring supported cylindrical shells under axial compression. Thin-Walled Structures 43 (3): 427–443.
Zhang, X. M., Liu, G.R. & Lam, K.Y. 2001. Vibration Analysis of Cylindrical Shells Using the Wave Propagation Approach. Journal of Sound and Vibration 239 (3): 397–401.
Zhao, X., Liew, K. M. & Ng, T. Y. 2002. Vibrations of rotating cross-ply laminated circular cylindrical shells with strings and ring stiffeners. International Journal of Solids and Structures 39: 529–545.
Author information
Authors and Affiliations
Corresponding author
Appendix-I:
Appendix-I:
where
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Arshad, S., Naeem, M. & Soutis, C. Influence of ring support on free vibration of sandwich functionally graded cylindrical shells with middle layer of isotropic material. J Engin Res 4, 9 (2016). https://doi.org/10.7603/s40632-016-0009-z
Revised:
Accepted:
Published:
DOI: https://doi.org/10.7603/s40632-016-0009-z