Comparison of Various Shell Theories for Vibrating Functionally Graded Cylindrical Shells

Document Type : Research Paper

Author

Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch

Abstract

The classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type solution method for a functionally graded cylindrical shell with simply supported edges. The effects of transverse shear deformation, geometric size, and configurations of the constituent materials on the natural frequencies of the shell are investigated. Validity of present formulation was checked by comparing the numerical results with the Love’s shell theory.

Keywords

[1] Reddy J.N., Khdeir A.A., 1989, Buckling and vibration of laminated composite plates using various plate theories, AIAA Journal 27(12): 1808-1817.
[2] Sivadas K.R., Ganesan N., 1991, Vibration analysis of laminated conical shells with variable thickness, Journal of Sound and Vibration 148(3): 477-491.
[3] Matsunaga H., 1999, Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses, Journal of Sound and Vibration 225(1): 41-60.
[4] Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.
[5] Pradhan S.C., Loy C.T., Lam K.Y., Reddy J.N., 2000, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics 61: 111-129.
[6] 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.
[7] Patel B.P., Gupta S.S., Loknath M.S., Kadu C.P., 2005, Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory, Composite Structures 69(3): 259-270.
[8] Haddadpour H., Mahmoudkhani S., Navazi H.M., 2007, Free vibration analysis of functionally graded cylindrical shells including thermal effects, Thin-Walled Structures 45(6): 591-599.
[9] Kadoli R., Ganesan N., 2006, Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition, Journal of Sound and Vibration 289(3): 450-480.
[10] Zhi-yuan C., Hua-ning W., 2007, Free vibration of FGM cylindrical shells with holes under various boundary conditions, Journal of Sound and Vibration 306(1-2): 227-237.
[11] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, FL, Second Edition.