Application of Ritz method for vibration analysis of stepped functionally graded spherical torus shell with general boundary conditions. (1st July 2020) - Gong, Qingtao; Li, Haichao; Chen, Hailong; Teng, Yao; Wang, Na
Abstract: This paper presents a generalized formulation to analyze the free vibration characteristics of stepped functionally graded spherical torus shell based on the Ritz method. Two kinds of the functionally graded model are considered in this study, and the first-order shear deformation theory (FSDT) is adopted to obtain the displacement fields of the model. The accurate results can be guaranteed by using domain decomposition method, in which the displacement functions component along axial direction and circumferential direction are respectively represented by unified Jacobi polynomials and Fourier series. In addition, the spring stiffness method is applied to simulate various complex boundary conditions, and the final solutions can be obtained by using Ritz method. The results of the same condition are compared with the numerical results which obtained by finite element method (FEM) and published literatures to verify the validation of the present method. On this basis, the vibration characteristics of stepped functionally graded spherical torus shell with general boundary conditions are further studied by a series of numerical examples.