A unified formulation for dynamic behavior analysis of spherical cap with uniform and stepped thickness distribution under different edge constraints. (January 2020) - Du, Yuan; Pang, Fuzhen; Sun, Liping; Li, Haichao
Abstract: The research introduces a unified method to investigate the dynamic behavior of spherical caps with uniform and stepped thickness under different edge constraints. In the framework of thin shell theory, the mathematical model of spherical cap is proposed. By combining the multi-section partition technique and Rayleigh-Ritz method, the vibration characteristics of spherical caps can be obtained. The spherical cap is partitioned into sections along the meridian direction, in which the displacement components of spherical caps along meridian and circumferential direction are respectively represented by Jacobi polynomials and Fourier series. Based on the virtual boundary spring stiffness technique, different edge conditions can be easily simulated. The comparison with FEM, modal test and published literatures prove the accuracy and dependability of current method. The impacts of geometric parameters and edge constraints on the vibration characteristics of spherical cap are also discussed. Highlights: Free vibration ofspherical cap with uniform and stepped thickness under complex edge constraintsisinvestigated by using ageneralizedsemianalytical method. Fast convergence, high accuracy and reliabilityof method presented in current research have been proved. The papergeneralizesthe selection of admissible displacement functions by using Jacobi polynomial. Different edge constraints can be easily simulated by virtualboundaryspring stiffness technique.