OICC Press Journal of Solid Mechanics 2008-7683 6 5 2014 12 30 Influence of the Elastic Foundation on the Free Vibration and Buckling of Thin-Walled Piezoelectric-Based FGM Cylindrical Shells Under Combined Loadings 347 365 EN M Mohammadimehr Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan M Moradi Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan A Loghman Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan Journal Article 2014 12 30 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.