In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

在本文中，开发了一种统一的方法来分析具有非均匀厚度的三层功能梯度圆柱壳的自由振动。中间层由二维功能梯度材料 (2D-FGM) 组成，其厚度设置为平滑连续性的函数。在壳的末端分配了四组人工弹簧以满足任意边界条件。Sanders 的壳理论用于获得应变和曲率-位移关系。此外，选择切比雪夫多项式作为容许函数以提高计算效率，并通过瑞利-里兹方法推导出运动方程。弹簧刚度、体积分数指标、构型对壳体的影响，