Vibration of Functionally Graded Cylindrical Shells Under Effect Clamped-Free Boundary Conditions Using Hamilton's Principle

In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions





References:
[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.