Development of a Finite Element Model for a Guided Spherical Shell

Abstract

A doubly curved anisymmetric spherical-shell finite element is utilized in order to predict the dynamic response of spherical shells for the Class V flextensional underwater acoustic transducer. The spherical shell is represented as a finite number of spherical frustra, joined at nodal circles. Norozhilov's “Thin Shell Theory” is applied and the element stiffness and mass matrices are derived and numerically integrated by utilizing Gauss-Legendre polynomials. The frequency coefficients of a spherical shell are defined. An IBM 360/75 computer is used for obtaining numerical results for varying thickness and opening angle, with guided clamped, guided pinned, clamped, and pinned boundary conditions. Numerical results for the Class V flextensional underwater transducer shell are included. Finally, a convergent test is carried out for a different number of finite elements for the Class V flextensional underwater transducer shell having pinned boundary conditions. The results agreed almost perfectly with earlier results obtained experimentally.