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Clamped-clamped Boundary Conditions for Analysis Free Vibration of Functionally Graded Cylindrical Shell with a Ring based on Third Order Shear Deformation Theory

Authors: M.Pourmahmoud, M.Salmanzadeh, M.Mehrani, M.R.Isvandzibaei


In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, cylindrical shell, Hamilton'sprinciple, Ring support

Digital Object Identifier (DOI):

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[1] Arnold, R.N., Warburton, G.B., 1948. Flexural vibrations of the walls of thin cylindrical shells. Proceedings of the Royal Society of London A; 197:238-256.
[2] Ludwig, A., Krieg, R., 1981.An analysis quasi-exact method for calculating eigen vibrations of thin circular shells. J. Sound vibration; 74,155-174.
[3] Chung, H., 1981. Free vibration analysis of circular cylindrical shells. J. Sound vibration; 74, 331-359.
[4] Soedel, W., 1980.A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions. J. Sound vibration; 70,309-317.
[5] Forsberg, K., 1964. Influence of boundary conditions on modal characteristics of cylindrical shells. AIAA J; 2, 182- 189.
[6] Lam, K.L., Loy, C.T., 1995. Effects of boundary conditions on frequencies characteristics for a multi- layered cylindrical shell. J. Sound vibration; 188, 363-384.
[7] Loy, C.T., Lam, K.Y., 1996.Vibration of cylindrical shells with ring support. I.Joumal of Impact Engineering; 1996; 35:455.
[8] Koizumi, M., 1993. The concept of FGM Ceramic Transactions, Functionally Gradient Materials.
[9] Makino A, Araki N, Kitajima H, Ohashi K. Transient temperature response of functionally gradient material subjected to partial, stepwise heating. Transactions of the Japan Society of Mechanical Engineers, Part B 1994; 60:4200-6(1994).
[10] Anon, 1996.FGM components: PM meets the challenge. Metal powder Report. 51:28-32.
[11] Zhang, X.D., Liu, D.Q., Ge, C.C., 1994. Thermal stress analysis of axial symmetry functionally gradient materials under steady temperature field. Journal of Functional Materials; 25:452-5.
[12] Wetherhold, R.C., Seelman, S., Wang, J.Z., 1996. Use of functionally graded materials to eliminate or control thermal deformation. Composites Science and Technology; 56:1099-104.
[13] Najafizadeh, M.M., Hedayati, B. Refined Theory for Thermoelastic Stability of Functionally Graded Circular Plates. Journal of thermal stresses; 27:857-880.
[14] Soedel, W., 1981. Vibration of shells and plates. MARCEL DEKKER, INC, New York.
[15] Loy, C.T., Lam, K.Y., Reddy, J.N., 1999.Vibration of functionally graded cylindrical shells; 41:309-324.
[16] 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.