Free vibration analysis of bi-directional functionally graded cylindrical shells with varying thickness

Abstract

The article presents a semi-analytical solution for the free vibration problem in bi-directional functionally graded (FG) cylindrical shells with varying thickness, utilizing a modified shear deformation shell theory (MSDT). In this model, the mechanical properties of the cylindrical shells change along both the axial and thickness directions. Classical analytical methods for shell structures often face limitations in terms of boundary conditions, transverse shear deformation, and rotary inertia, making the use of MSDT and Galerkin procedure necessary for solving the problem of free vibration analysis in this study. The boundary conditions of the bi-directional FG cylindrical shells are chosen to be simply supported and clamped, and the presented method is compared to relevant results in the literature to validate its effectiveness. Moreover, a comprehensive parametric investigation is conducted to evaluate the influence of material and geometrical parameters on the natural frequencies. The results show that the natural frequency of the FG cylindrical shells is significantly affected by the material and geometrical parameters, including the power-law index, the thickness variation, the aspect ratio, and the boundary conditions.