In this article, a semi-analytical solution is provided to investigate the free vibration characteristics of rotating truncated conical shells surrounded by a Winkler–Pasternak type foundation. It is assumed that the material of the shell is composed of epoxy as matrix and graphene nanoplatelets (GPLs) as reinforcement dispersed in both thickness and length directions of the shell. The shell is modeled based on first-order shear deformation theory and the equivalent mechanical properties are evaluated using the rule of the mixture and the Halpin–Tsai model. The governing equations are derived by implementing Hamilton’s principle incorporating centrifugal acceleration, Coriolis acceleration, and the initial hoop tension. Utilizing trigonometric functions, an analytical solution is presented to solve the governing equations in the circumferential direction and a numerical solution is provided in the longitudinal direction by utilizing differential quadrature method. The convergence and accuracy of the present results are examined with those available in the literature. A parametric study is provided to check the influences of boundary conditions, rotational speed, circumferential wave number, mass fraction and dispersion pattern of the GPLs, and Winkler and shear coefficients of the foundation on the natural frequencies of the shell. It is concluded that an increment in the mass fraction of the GPLs increases the natural frequencies and the GPLs scattering near the inner surface and the small radius of the shell have a higher reinforcing effect.

在本文中，提供了一种半解析解来研究由 Winkler-Pasternak 型基础包围的旋转截锥壳的自由振动特性。假设外壳的材料由环氧树脂作为基质和石墨烯纳米片 (GPL) 作为增强材料组成，分散在外壳的厚度和长度方向。基于一阶剪切变形理论对壳进行建模，并使用混合物规则和 Halpin-Tsai 模型评估等效力学性能。控制方程是通过实施包含离心加速度、科里奥利加速度和初始环张力的哈密顿原理推导出来的。利用三角函数，提出了求解圆周方向控制方程的解析解，并利用微分正交法在纵向方向上给出了数值解。本结果的收敛性和准确性用文献中可用的那些进行了检查。提供参数研究以检查边界条件、转速、圆周波数、GPL 的质量分数和分散模式以及基础的温克勒系数和剪切系数对壳体固有频率的影响。得出的结论是，GPLs 质量分数的增加会增加固有频率，并且 GPLs 在内表面附近散射和壳的小半径具有更高的增强效果。