Nonlinear Vibration Analysis of a Cylindrical FGM Shell on a Viscoelastic Foundation under the Action of Lateral and Compressive Axial Loads

Document Type : Persian


Assistant Professor of Mechanical and Aerospace Engineering, Ph.D. of Aerospace Engineering, Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Tehran, Iran


In this paper, the nonlinear vibration analysis of a thin cylindrical shell made of Functionally Graded Material (FGM) resting on a nonlinear viscoelastic foundation under compressive axial and lateral loads is studied. Nonlinear governing coupled partial differential equations of motions (PDEs) for cylindrical shell are derived using improved Donnell shell theory. The equations of motions (EOMs) then are solved using the Galerkin method, Volmir’s assumption and the forth-order Runge-Kutta method to obtain dynamic response of the shell including nonlinear frequencies, frequency-amplitude curves and nonlinear radial deflection for the shell of revolution. Afterward, the effect of changing the value of different parameters on the nonlinear dynamic response of the FGM cylindrical shell considering compressive axial and lateral loads, geometric characteristics of the shell, FGM material distribution along direction of the thickness of the shell and coefficients of the viscoelastic foundation are all investigated


[1] Soldatos K.P., Hajigeoriou V.P., Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels, Journal of Sound and Vibration, Vol. 137, 1990, pp. 369-384.
[2] Soldatos K.P., A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels, Journal of Sound and Vibration,Vol. 97, 1984, pp. 305-319.
[3] Lam K.Y., Loy C.T., Effects of boundary conditions on frequencies characteristics for a multi-layered cylindrical shell, Journal of Sound and Vibration, Vol. 188, 1995, pp. 363-384.
[4] Loy C.T., Lam K.Y., Shu C., Analysis of cylindrical shells using generalized differential quadrature, Shock and Vibration, Vol. 4, 1997, pp. 193-198.
[5] Soedel W., A new frequency formula for closed circular cylindrical shells for large variety of boundary conditions, Journal of Sound and Vibration, Vol. 70, No. 3, 1980, pp. 309-317.
[6] Loy C.T., Lam K.Y., Vibration of cylindrical shells with ring support, International Journal of Mechanical Science, Vol. 39, 1997, pp. 455-471.
[7] Bakhtiari-Nejad F., Mousavi Bideleh S.M., Nonlinear free vibration analysis of pre-stressed circular cylindrical shells on the Winkler-Pasternak foundation, Thin-Walled Structures, Vol. 53, 2012, pp. 26–39.
[8] Paliwal D.N., Large amplitude free vibrations of cylindrical shell on Pasternak foundations, International Journal of Pressure Vessels & Piping, Vol. 54, 1993, p.p. 387-398.
[9] Pradhan S.C., Loy C.T., Lam K.Y., Reddy J.N., Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics, Vol. 61, 2000, pp. 111-129.
[10] Loy C.T., Lam K.T., Reddy J.N., Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences Vol. 41, 1999, pp. 309-324.
[11] Ravikiran Kadoli, Ganesan N., Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition, Journal of Sound and Vibration,Vol. 289, 2006, pp. 450-480.
[12] Haddadpour H., Mahmoudkhani S., Navazi H.M., Free vibration analysis of functionally graded cylindrical shells including thermal effects, Thin-Walled Structures, Vol. 45, 2007, pp. 591-599.
[13] Shen. S.-H., Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium, International Journal of Mechanical Sciences, Vol. 51, No. 5, 2009, pp. 372-383.
[14] Bagherizadeh E., Kiani Y., Eslami M.R., Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures, Vol. 93, No. 11, 2011, pp. 3063-3071.
[15] Shen. S.-H., Wang H., Nonlinear vibration of shear deformable FGM cylindrical panels resting on elastic foundations in thermal environments, Composites Part B: Engineering, Vol. 60, 2014, pp. 167-177.
[16] Bich D.H., Long V.D., Non-linear dynamical analysis of imperfect functionally graded material shallow shells, Vietnam Journal of Mechanics, VAST, Vol. 32, No. 1, 2010, pp. 1-14.
[17] Bich D.H., Xuan N.N., Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations, Journal of Sound and Vibration, Vol. 331, 2012, pp. 5488-5501.
[18] Volmir A.S., Nonlinear Dynamics of Plates and Shells, Science Edition, 1972.