Vibration analysis of truncated spherical shells under various edge constraints. (February 2020) - Du, Yuan; Sun, Liping; Li, Shuo; Li, Yuhui
Abstract: By means of combining Flügge's thin shell theory and energy method, a generalized approach to investigate vibration characteristic of truncated spherical shell subjected to various edge constraints is proposed. The truncated spherical shell is devided into different sections along the meridian line, in which the displacement function of truncated spherical shell along meridian and circumferential line are respectively represented by Jacobi polynomials and Fourier series. Various edge constraints can be simulated on the basis of virtual spring stiffness method in the current research. Finally, the solutions can be derived by meand of Ritz method. The dependability and exactness of current method have been proved by the comparison between current method, FEM and related literatures. The dimensionless frequency parameters of different truncated spherical shell under various edge constraints are displayed. In addition, the influence of geometric dimensions and boundary constraints on frequency parameters are also discussed. Highlights: Free vibration of truncated spherical shells with uniform and stepped thickness under classical and elastic boundary conditions is studied by means of a generalized semi analytical method. The admissible displacement function is expressed as a unified formulation. Different boundary constraints can be easily simulated by the method presented in the current research. The method presented in the current research converges well and has high accuracy.