Influence of the Elastic Foundation on the Free Vibration and Buckling of Thin-Walled Piezoelectric-Based FGM Cylindrical Shells Under Combined Loadings

Document Type : Research Paper


Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan


In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell's equations and the Navier's type solution used to solve these equations. Material properties are changed according to power law in the direction of thickness. In this study, the effects of Pasternak elastic foundation coefficients and also the effects of material distribution, geometrical ratios and loading conditions on the natural frequencies are studied. It is observed that by increasing Pasternak elastic medium coefficients, the natural frequencies of functionally graded piezoelectric materials (FGPM) cylindrical shell always increases. The mode shapes of FGPM cylindrical shell has been shown in this research and the results show that the distribution of the radial displacements is more significant than circumferential and longitudinal displacements.


[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, Functionally gradient materials, Proceedings of the first International Symposium on Functionally Gradient Materials 327-332.
[2] Koizumi M., 1993, The concept of FGM ceramic transactions, Functionally Graded Materials 34: 3-10.
[3] Pasternak P., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvenneo Izdatelstvo Literaturi po Stroitelstvu Arkhitekture, Moscow, USSR.
[4] Loy CT., Lam KY., Reddy JN., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.
[5] Pradhan SC., Loy CT., Lam KY., Reddy JN., 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] Shah AG., Mahmood T., Naeem MN., Iqbal Z., Arshad SH., 2009, Vibrations of functionally graded cylindrical shells based on elastic foundations, Acta Mechanica 211: 293-307.
[8] Bhangale RK., Ganesan N., 2005, Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells, Journal of Sound and Vibration 288: 412-422.
[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: 450-480.
[10] Malekzadeh P., Heydarpour Y., 2012, Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment, Composite Structures 94: 2971-2981.
[11] Ebrahimi MJ., Najafizadeh MM., 2014, Free vibration analysis of two-dimensional functionally graded cylindrical shells, Applied Mathematical Modelling 38: 308-324.
[12] Sheng GG., Wang X., 2013, Nonlinear vibration control of functionally graded laminated cylindrical shells, Composites Part B: Engineering 52: 1-10.
[13] Du C., Li Y., 2013, Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments, Composite Structures 102: 164-174.
[14] Sofiyev AH., Kuruoglu N., 2013, Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium, Composites Part B: Engineering 45: 1133-1142.
[15] Sheng GG., Wang X., 2013, An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads, Composite Structures 97: 261-268.
[16] Rafiee M., Mohammadi M., Aragh BS., Yaghoobi H., 2013, Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Composite Structures 103: 188-196.
[17] Ghorbanpour Arani A., Bakhtiari R., Mohammadimehr M., Mozdianfard M.R., 2011, Electromagnetomechanical responses of a radially polarized rotating functionally graded piezoelectric shaft, Turkish Journal of Engineering & Environmental Sciences 36(1): 33-44.
[18] Khoshgoftar MJ., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Material Structures 18: 115007-115015.
[19] Sheng GG., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34: 2630-2643.
[20] Fernandes A., Pouget J., 2006, Structural response of composite plates equipped with piezoelectric actuators, Computer and Structures 84: 1459-1470.
[21] Bagherizadeh E., Kiani Y., Eslami M.R., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93: 3063-3071.
[22] Pouresmaeeli S., Fazelzadeh S.A., Ghavanloo E., 2012, Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium, Composites Part B: Engineering 43: 3384-3390.
[23] Jafari A.A., Khalili S.M.R., Azarafza R., 2005, Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads, Thin-Walled Structures 43: 1763-1786.
[24] Dong K., Wang X., 2007, Wave propagation characteristics in piezoelectric cylindrical laminated shells under large deformation, Composite Structures 77: 171-181.
[25] Ghorbanpour Arani A., Fesharaki J.J., Mohammadimehr M., Golabi S., 2010, Electro-magneto-thermo-mechanical behaviors of a radially polarized FGPM thick hollow sphere, Journal of Solid Mechanics 2: 305-315.
[26] Heyliger P., 1997, A note on the static behavior of simply supported laminated piezoelectric cylinders, International Journal of Solid and Structures 34: 3781-3794.
[27] He Y., 2004, Heat capacity, thermal conductivity, and thermal expansion of barium titanate-based ceramics, Thermochimica Acta 419: 135-141.
[28] Ramirez F., Heyliger P.R., Pan E., 2006, Free vibration response of two-dimensional magneto-electro-elastic laminated plates, Journal of Sound and Vibrations 292: 626-644.
[29] Arani A.G., Jafarzadeh Jazi A., Abdollahian M., Mozdianfard M.R., Mohammadimehr M., Amir S., Exact solution for electrothermoelastic behaviors of a radially polarized FGPM Rotating Disk, Journal of Solid Mechanics 3: 244-257.
[30] Timoshenko S.P., 1922, On the transverse vibrations of bars of uniform cross-section, Philosophical Magazine 43: 125-131.