Influence of Power Law Distribution with Pressure on the Frequencies of Supported Functionally Graded Material Cylindrical Shell with C-SL and F-SS Boundary Conditions

Document Type : Research Paper


Department of Mechanical Engineering, Andimeshk Branch, Islamic Azad University


In this paper, influence power-law distribution with pressure on frequencies of the supported functionally graded cylindrical shell is studied. This shell is constructed from a functionally graded material (FGM) with two constituent materials. FGMs are graded through the thickness direction, from one surface of the shell to the next. The supported FGM shell equations are created based on FSDT. The governing equations of the movement were utilized by the Ritz method. The boundary conditions are clamp-sliding and free-simply support. The influence of the various values of the power-law distribution with pressure supported and different conditions on the frequencies characteristics are studied. This study shows that the frequencies decreased with the increase in the amounts of the power-law distribution with pressure. Thus, the constituent power-law distribution with pressure effects on the frequencies. The results show the frequencies with different power-law distribution under pressures are various for different conditions.


Main Subjects

[1] Sechler, E.E., 1974. Thin-shell structures theory experiment and design. Englewood Cliffs, NJ: Prentice-Hall, California.
[2] Yan, J., Li, T.Y., Liu, T.G. & Liu, J.X. 2006. Characteristics of the vibrational power flow propagation in a submerged periodic ring-stiffened cylindrical shell. Applied Acoustics. (67): 550-569.
[3] Wang, R.T. & Lin, Z.X. 2006. Vibration analysis of ring-stiffened cross-ply laminated cylindrical shells. Jouranl of Sound and Vibration. (295): 964-987.
[4] Pan, Z., Li, X. & Ma, J. A. 2008. Study on free vibration of a ring-stiffened thin circular cylindrical shell with arbitrary boundary conditions. Jouranl of Sound and Vibration.   (314): 330-342.
[5] Gan, L., Li, X. & Zhang, Z. 2009. Free vibration analysis of ring-stiffened cylindrical shells using wave propagation approach. Jouranl of Sound and Vibration. (326): 633-646.
[6] Zhou, X. 2012. Vibration and stability of ring-stiffened thin-walled cylindrical shells conveying fluid. Acta Mechanica Solida Sinica. (25): 168-176.
[7] Qu, Y., Chen, Y., Long, X., Hua, H. & Meng, G. 2013. A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations. European Journal of Mechanics endash; A/Solids. (37): 200-215.
[8] Love, A.E.H. 1944. A treatise on the mathematical theory of elasticity [M]. New York: Dover Publication.
[9] Leissa, A.W. 1993. Vibration of shells. NASA SP-288, 1973; Reprinted by Acoustical Society of America, America Institute of Physics.
[10] Blevins, R.D. 1979. Formulas for natural frequency and mode shape. Van Nostrand Reinhold, New York.
[11] Soedel, W. 1980. A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions. Jouranl of Sound and Vibration. (70): 309-317.
[12] Chung, H. 1981. Free vibration analysis of circular cylindrical shells. Jouranl of Sound and Vibration. (74): 331-359.
[13] Reddy, J.N. 2004. Mechanics of laminated composite plates and shells. 2nd edn. CRC Press, New York.
[14] Forsberg, K. 1964. Influence of boundary conditions on modal characteristics of cylindrical shells. AIAA Journal. (2): 182-189.
[15] Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. & Ford, R.G. 1999. Functionally graded materials: design, processing and applications, Kluwer Academic Publishers, London.
[16] Loy, C.T., Lam, K.Y. & Reddy, J.N. 1999. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences. (41): 309–324.
[17] Patel, B.P., Gupta, S.S., Loknath, M.S. & Kadu, C.P. 2005. Free vibration analysis of functionally graded elliptical cylindrical shells using higher order theory. Composite Structures. (69): 259–270.
[18] Zhi, C. & Hua, W. 2007. Free vibration of FGM cylindrical shells with holes under various boundary conditions. Jouranl of Sound and Vibration. (306): 227–237.
[19] Arshad, S. H., Naeem, M. N., & Sultana, N. 2007. Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. (221): 1483–1495.
[20] Shah, A.G., Mahmood, T. & Naeem, M.N. 2009. Vibrations of FGM thin cylindrical shells with exponential volume fraction law. Applied Mathematics and Mechanics (English Edition). (5): 607–615.
[21] Hosseini-Hashemi, sh., Ilkhani,M.R and Fadaee. M. Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell. International Journal of Mechanical Sciences 76 (2013) 9–20.
[22] Amirabadi, H., Farhatnia, F., Eftekhari, S.A., Hosseini-Ara, R. 2020. Free vibration analysis of rotating functionally graded GPL-reinforced truncated thick conical shells under different boundary conditions. Mechanics Based Design of Structures and Machines, Published online: 30 Sep 2020. pp. 1-32.
[23] Mohamadi, B., Eftekhari, S.A., Toghraie, D. 2020.  Numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid. International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 4, pp. 1689-1723.
[24]Amirabadi, H., Farhatnia, F., Eftekhari, S.A., Hosseini-Ara, R. 2021. Wave propagation in rotating functionally graded GPL-reinforced cylindrical shells based on the third-order shear deformation theory. Waves in Random and Complex Media, Published online: 03 Feb 2021.
[25] Soedel, W. 2004. Vibration of shells and plates. 3rd edn. Marcel Dekker Inc, New York.
[26] Reddy, J.N. 2004. Mechanics of laminated composite plates and shells: Theory and analysis, 2nd ed. CRC Press, Boca Raton.