Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis

Abstract

The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material (FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded (FG), the material properties vary along the thickness direction as one innovation of this study. Applying the first-order shear deformation theory (FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations (PDEs) using Hamilton’s principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material (FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.