In this paper, the Ritz method is adopted to investigate the vibration characteristics of isotropic moderately thick annular spherical shell with general boundary conditions. The energy expressions of the annular spherical shell were established based on the first-order shear deformation theory (FSDT). The spring stiffness method is introduced to guarantee continuity and simulate various boundary conditions on the basis of the domain decomposition method. Under the current framework, the displacement admissible function along axial direction and circumferential direction of the shell structure are, respectively, expanded as the unified Jacobi polynomials and Fourier series. The final solutions can be obtained according to the Ritz method. The validity of the proposed method is proved by comparing the results of the same condition with those obtained by the finite element method (FEM) and published literatures. The results show that the current method has fast convergence and delightful accuracy through the comparative study. On this basis, the vibration characteristics of isotropic moderately thick annular spherical shell are further studied by a series of numerical examples.

中文翻译：

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基于Ritz方法的具有一般边界条件的中厚球壳的自由振动特性

本文采用Ritz方法研究了在一般边界条件下各向同性的中等厚度环形球壳的振动特性。基于一阶剪切变形理论（FSDT）建立了环形球壳的能量表达式。引入弹簧刚度法以保证连续性，并在域分解法的基础上模拟各种边界条件。在当前框架下，沿壳体结构的轴向和周向的位移容许函数分别扩展为统一的Jacobi多项式和Fourier级数。最终解决方案可以根据Ritz方法获得。通过将相同条件下的结果与有限元方法（FEM）和已发表的文献进行比较，证明了该方法的有效性。结果表明，通过比较研究，该方法收敛速度快，精度高。在此基础上，通过一系列数值实例，进一步研究了各向同性中等厚度的环形球壳的振动特性。