### Comparison of Two Kinds of Functionally Graded Cylindrical Shells with Various Volume Fraction Laws for Vibration Analysis

Document Type: Research Paper

Authors

Department of Mechanical Engineering, Sinhgad College of Engineering, University of Pune

Abstract

In this paper, a study on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are taken into account by studying the frequencies of two FG cylindrical shells. Type I FG cylindrical shell has nickel on its inner surface and stainless steel on its outer surface and Type II FG cylindrical shell has stainless steel on its inner surface and nickel on its outer surface. The study is carried out based on third order shear deformation shell theory (TSDT). The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. The analysis is carried out with strains-displacement relations from Love's shell theory. The governing equations are obtained using energy functional with the Rayleigh-Ritz method. Results are presented on the frequency characteristics and the influences of constituent various volume fractions for Type I and II FG cylindrical shells and simply supported boundary conditions on the frequencies.

Keywords

[1] Arnold R.N., Warburton G.B., 1948, Flexural vibrations of the walls of thin cylindrical shells, in: 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, Journal of Sound and Vibration 74:155-174.

[3] Chung H., 1981, Free vibration analysis of circular cylindrical shells, Journal of Sound and Vibration 74: 331-359.

[4] Soedel W., 1980, A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration 70:309-317.

[5] Forsberg K., 1964, Influence of boundary conditions on modal characteristics of cylindrical shells, AIAA Journal 2:182-189.

[6] Bhimaraddi A., 1984, A higher order theory for free vibration analysis of circular cylindrical shells, International Journal of Solids and Structures 20: 623-630.

[7] Soldatos K.P., 1984, A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels, Journal of Sound and Vibration 97: 305-319.

[8] Bert C.W., Kumar M., 1982, Vibration of cylindrical shell of biomodulus composite materials, Journal of Sound and Vibration 81: 107-121.

[9] Soedel W., 1981, Vibration of Shells and Plates, Marcel Dekker Inc, New York, USA.

[10] Makino A., Araki N., Kitajima H., Ohashi K., 1994, Transient temperature response of functionally gradient material subjected to partial, stepwise heating, Transactions of the Japan Society ofMechanical Engineers, Part B 60: 4200-4206.

[11] Koizumi M., 1993, The concept of FGM, Ceramic Transactions, Functionally Gradient Materials 14: 3-10.

[12] Anon, 1996, FGM components: PM meets the challenge, Metal powder Report 51: 28-32.

[13] Obata Y., Noda N., 1994, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal stresses 17: 471-487.

[14] Takezono S., Tao K., Inamura E., Inoue M., 1996, Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid, JSME International Journal of Series A: Mechanics and Material Engineering 39: 573-581.

[15] 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: 1099-1104.

[16] 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: 452-455.

[17] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, in: Proceedings of the First International Symposium on Functionally Gradient Materials, 327-332, Japan.

[18] 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.

[19] Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.