Effect of Geometrical Parameters on Natural Frequencies of FGM Cylindrical shell with Holes Under Various Boundary Conditions

In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In this paper, free vibration of thin functionally graded cylindrical shell with hole composed of stainless steel and zirconia is studied. The mechanical properties vary smoothly and continuously from one surface to the other according to a volume fraction power-law distribution. The Influence of shell geometrical parameters, variations of volume fractions and boundary conditions on natural frequency is considered. The equations of motion are based on strains-displacement relations from Love-s shell theory and Rayleigh method. The results have been obtained for natural frequencies of cylindrical shell with holes for different shape, number and location in this paper.

• Mostafa Ghayour
• Mohammad Sadegh Golabi

• Functionally gradient material
• Vibration
• various boundary conditions
• cylindrical shells.

[1] Koizumi M., Functionally gradient materials the concept of FGM.
Ceramic Transactions, Vol (34), 1993;pp 3-10
[2] Anon, FGM components: PM meets the challenge. Metal Powder
Report, Vol 51, 1996; pp 28-32..
[3] Ootao Y., Tanigawa Y., Nakamura T., Optimization of material
composition of FGM hollow circular cylinder under thermal loading: a
neural network approach, Composites Part B 30 (1999) 415-422.
[4] Kadoli R., Ganesan N., Buckling and free vibration analysis of
functionally graded cylindrical shells subjected to a temperature
specified boundary condition, Journal of Sound and Vibration 289
(2006) 450-480.
[5] Loy C.T., Lam K.Y., Reddy J.N., Vibration of functionally graded
cylindrical shells, International Journal of Mechanical Sciences 41
(1999) 309-324
[6] Prandhan S.C., Loy C.T., Lam K.Y., Reddy J.N., Vibration
characteristics of FGM cylindrical shells under various boundary
condition, Applied Acoustics 61 (2000) 111-129
[7] Shah A.G., Mohmood T., Naeem M.N., Vibrations of FGM thin
cylindrical shells with exponential volume fraction law, Applied
Mathematics and Mechanics, 30(5), (2009), 607-615
[8] Patel B.P., Gupla S.S., Moknath M.S., Free vibration analysis of FGM
elliptical cylindrical shells, Composite Structure, 69 , (2005), 259-270
[9] Zhi-yuan C., Hua-ning W., Free vibration of FGM cylindrical shells
with holes under various boundary conditions, Journal of Sound and
Vibration 306 (2007) 227-237
[10] Shahsiah R., Eslami M.R., Thermal buckling of functionally graded
cylindrical shell, Journal of Thermal Stresses 26 (2003) 277-294.
[11] Touloukian YS. Thermo physical properties of high temperature solid
materials. New York: Macmillan, 1967.
[12] Love AEH. A treatise on the mathematical theory of elasticity.
4th Ed. Cambridge: Cambridge University Press, 1952,
[13] Roa S.S., Vibration of continuous systems, John Wiley & Sons, Inc.,
Hoboken, New Jersey, 2007, 540-605