Numerical Method for Vibration Analysis of Cylindrical Shells

Abstract

A relatively simple, yet effective, formulation and numerical methodology is proposed for the vibration analysis of thin-walled cylindrical shells subjected to any variationally consistent set of boundary conditions at the boundaries. Using the Budiansky-Sanders first-order shell theory and adopting as fundamental variables those quantities that describe the geometric and natural boundary conditions on a rotationally symmetric edge of the shell, a system of eight first-order differential equations is derived. A numerical procedure based on the basic ideas of the hierarchical finite-element method is proposed for the solution of the resulting two-point boundary-value problem. The elected set of fundamental variables together with the proposed modal solution allows one to satisfy all natural and geometric boundary conditions exactly and obtain all displacements and internal forces simultaneously and with the same degree of accuracy. This method, in which the shell is treated as a macroelement, offers distinctive computational advantages over other numerical and analytical methods found in literature for the analysis of the influence of boundary conditions on the modal characteristics of thin cylindrical shells. Application of the method to a few selected cases and comparisons of the numerical results with those obtained by other theories and experiments are found to be good, and to demonstrate the effectiveness and accuracy of this methodology.