A Parametric Study for Vibration Analysis of Composite Cylindrical Shell Resting under Elastic Foundation: Analytical and Numerical Methods


Composite Materials & Technology Center, Malek-e-Ashtar University of Technology


The aim of this study is to investigatethe effective parameters on vibrations of circular cylindrical shells with fixed rotary speed andresting elastic foundation by means of analytical and finite element numerical simulation. First, the governing equations are derived using the theory of Donnell, considering the centrifugal forces,Coriolis acceleration, and the initial annular tension. Then, the analytical solution for cylindrical shells isintroduced under simply supported conditions. Further, the effect of parameters such as therotational speed of the shell, its lay-up, fiber angle, and the stiffness of the elastic foundation on the values of natural frequency and the critical velocity of the shells are studied. The analytical solution results are in good compatibility with the results achieved from the finite element method.


Article Title [فارسی]

Vibration analysis, Annular cylindrical shells, Donnel theory, Analytical solution, Finite element

[1]   Egle, D.M., Sewall, J.L., “An Analysis of the Free Vibration of Orthogonally sti. Enedcylindrical Shells with sti. Eners Treated as Discrete Elements”, AIAA Journal, Vol. 3, 1968, pp. 518- 26.
[2]   Rinehart, S.A. and Wang, J.T.S., “Vibration of Simply Supported Cylindrical Shells with Longitudinal Stiffeners,” Journal of Sound and Vibration, Vol. 24, No. 2, 1972, pp.151-163
[3]   Amabili, M., “Nonlinear Vibrations of Circular Cylindrical Shells with Different Boundary Conditions,” AIAA Journal, Vol. 41, No. 6, 2003, pp. 1119-1130
[4]   Karagiozisa, K.N., Amabili, M., Padoussisa, M.P., and Misra, A.K., “Nonlinear Vibrations of Fluid-Filled Clamped Circular Cylindrical Shells,” Journal of Fluids and Structures, Vol. 21, 2005, pp. 579–595.
[5]   Pellicano, F., , “Linear and Nonlinear Vibrations of Shells,” 2nd International Conference on Nonlinear Normal Modes and Localization in Vibrating Systems,” Samos, June 19-23, 2006.
[6]   Shao, Z.S., and Ma, G.W., “Series Expansion Method Free Vibration Analysis of Laminated Cylindrical Shells by Using Fourier, Journal of Thermoplastic Composite Materials, Vol. 20, No. 551, 2007
[7]   Eipakchi, H.R., Rahimi, G.H., Esmaeilzadeh Khadem, S., ,“Closed form Solution for Displacements of Thick Cylindrs With Varying Thickness Subjected to Non-Uniform Internal Pressure”, J. Struc. Eng. and Mech., Vol. 16, No. 6, 2003, pp. 731-748.
[8]   Zhao, X., Liew, K.M., Ng, T.Y., “Vibration of Rotating Cross-Ply Laminated Circular Cylindrical Shells with Stringer and Ring Stiffeners”, Int. Journal of Solids and Structures, Vol. 39, 2002, pp. 529-545.
[9]   Jafari, A.A., and Bagheri, M., “Free Vibration of Rotating Ring Stiffened Cylindrical Shells with Non-Uniform Stiffener Distribution,” J Sound Vib, Vol. 296, 2006, pp. 353-376.
[10]    M.J. Ebrahimi, M.M., “Najafizadeh, Free Vibration Analysis of Two-Dimensional Functionally Graded Cylindrical Shells”, Applied Mathematical Modelling, Vol. 38, pp. 308–324.