Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

这项研究获得了圆锥球形功能梯度材料（FGM）壳的固有频率。假定圆锥壳和球形壳的组件具有相同的厚度。连接的壳体系统由FGM制成，其中壳体的属性沿厚度方向分级。壳的一阶剪切变形理论被用来研究剪切应变和旋转惯性的影响。采用唐纳尔运动学假设，借助汉密尔顿原理建立运动的一般方程以及相关的边界和连续性条件。使用半分析广义微分正交（GDQ）方法离散化所得的方程组。考虑壳体端部的各种边界条件和相交连续性条件，建立了一个特征值问题来检查振动频率。在利用常规有限元软件的数据证明了本发明方法对于薄各向同性均质连接壳的有效性和有效性之后，对由FGM和各种不同材料制成的中等厚度圆锥-球形连接壳组合系统进行了参数研究。终端支架的类型。