Free Vibration Analysis of FGM Cylindrical Shell with Supported Ring Based on Reddy Model under Clamped Boundary Condition

Document Type: Persian


1 Assistant Professor, Mechanical Engineering Department, Guilan University Ph.D. Student in Mechanical Engineering, Faculty member of, Islamic Azad University, Andimeshk Branch

2 Faculty Member of Mechanical Engineering, Islamic Azad University, Shushtar Branch

3 Faculty Member of Mechanical Engineering, Islamic Azad University, Izeh Branch


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. The properties are graded in the thickness direction according to a volume fraction power-law distribution.The cylindrical shells with 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
clamed-clamped boundary conditions.


[1]    Loy C.T., Lam, K.Y., Vibration of Cylindrical Shells with Ring Support, J. impact Engineering, 1996, Vol. 35, pp.455-463.

[2]  Xiang Y., Kitipornchai S., Lim C.W., Lau  C.W.H., Exact solutions for vibration of cylindrical shells with intermediate ring supports, Int. J. Mechanical Sciences,  Vol. 44(9),2002, pp.1907-1924.

[3]  Patel B.P., Gupla S.S., Moknath M.S., Free   Vibration analysis of FGM elliptical cylindrical shells, Composite structures, Vol. 69(3), 2004,  pp. 259-270.

[4]   Loy C.T., Lam K.Y., Reddy J.N., Vibration of functionally graded cylindrical shells. J. Mechanical Sciences, Vol.41 (3), 1999, pp. 309-324.

[5] Chen Q.W., Bian Z.G., Ding D.H., Three dimensional vibration analysis of fluid-filled Orthotropic FGM Cylindrical Shell. Journal of Mechanical Sciences, Vol 46, 2004, pp. 159-162.

[6]  Prandhan S.C., Log C.T., Lam K.Y., Reddy J.N., Vibration Characteristics of FGM Cylindrical Shells under Various Boundaries. Applied an Acoustics, 2000, Vol. 61, pp.117-126.

[7] Liew K.M., Kitipornchai S., Zhang X.Z., Analysis of the Thermal Stress Behavior of Functionally Graded Hollow Circular Cylinders. J. Functional Materials, 1994, Vol 25, pp. 452-465.

[8]   Sofiger A.H., Schanck E., The Stability of FG cylindrical shells under linearly increasing dynamic torsional loading, Engineering Structures, Vol. 26, 2004, pp.1323-1326.

[9]   Gong S.W., Lam K.Y., Reddy, J.N. The elastic response of FGM cylindrical shells low-velocity. J Impact Engineering, Vol.22 (4), 1999, pp. 397-417.

[10] Naeem M.N., Arshad S.H., The Ritz   formulation applied to the study of the    vibration frequency characteristics of   functionally graded circular cylindrical  shells,  J. Mechanical Engineering Science,   Vol. 224,Part C, , 2009, pp. 43-54.

[11] Mumtaz A., Muhammad N., Vibration Characteristics of Rotating FGM Circular Cylindrical Shells Using Wave Propagation Method. European Journal of Scientific Research, Vol. 36 ,No.2, 2009,  pp.184-235.

[12] Najafizadeh M.M., Isvandzibaei M.R., Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support. Acta Mechanica, Vol 191, 2007, pp. 75-91.

[13]  Soedel W., Vibration of shells and plates, Marcel Dekker, INC, New York, USA, 1981.

[14] Warburton G. B., Vibration of thin
cylindrical shells, J. Mechanical Engineering Science, Vol. 7, 1965, pp. 399-407.

[15]   Loy, C.T. Lam, K.Y. Reddy J.N., Vibration of functionally graded cylindrical shells. Int. J. Mechanical Sciences, Vol. 41, 1999, pp. 309-324.