A semi analytical solution for free vibration analysis of combined spherical and cylindrical shells with non-uniform thickness based on Ritz method

The paper investigated the free vibration of combined spherical-cylindrical-spherical (CSCS) shell with non-uniform thickness based on Ritz method. The energy method and first-order shear deformation theory are adopted to derive the formulas. The displacement functions are improved on base of domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement functions component along axial direction. The displacement functions component along circumferential direction is still Fourier series. In addition, the spring stiffness method is formed to be a unified format to deal with general boundary conditions. Then the final solutions are obtained by using Ritz method. To prove the validity of this method, the results of the same condition are compared with those obtained by FEM, published literatures and experiment. In addition, some meaningful examples are provided to reveal the free vibration characteristics of stepped spherical-cylindrical-spherical shell. The results of this paper can be used as the reference data for future research in related field.