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.

本文利用改进的剪切变形壳理论 (MSDT) 提出了具有不同厚度的双向功能梯度 (FG) 圆柱壳的自由振动问题的半解析解。在此模型中，圆柱壳的力学特性沿轴向和厚度方向发生变化。壳结构的经典分析方法往往在边界条件、横向剪切变形和旋转惯性方面面临局限性，因此必须使用 MSDT 和 Galerkin 程序来解决本研究中的自由振动分析问题。双向FG圆柱壳的边界条件选择简支夹紧，并将所提方法与文献中的相关结果进行比较，验证其有效性。而且，进行了全面的参数研究，以评估材料和几何参数对自然频率的影响。结果表明，FG 圆柱壳的固有频率受材料和几何参数的显着影响，包括幂律指数、厚度变化、纵横比和边界条件。