A unified semi-analytical method for vibration analysis of shells of revolution stiffened by rings with T cross-section

Abstract

A unified semi-analytical method is presented to study free and forced vibrations of arbitrary shells of revolution stiffened by rings with T cross-section. Combined shells of revolution and rings with rectangular and L cross-sections are included in the titled structure. The ring-stiffened shell is firstly decomposed to several shell segments and rings with T cross-section according to intersections between the shell and rings, and shell segments are further divided into some narrower segments to be treated as conical shells. Rings with T cross-section are modeled as two cylindrical shells (left and right flanges) and one annular plate (web), rather than conventional curved beams. Conical segments, cylindrical segments and annular plates are uniformly analyzed by employing Flügge thin shell theory and expanding displacements as power series. To consider both classic and elastic boundary conditions, the artificial spring technology is employed to restrain displacements at edges. Then, boundary conditions at two edges and a set of continuity conditions of adjacent segments are assembled to the final governing equation. Through comparing free and forced vibration results of present method with the ones in the literature and calculated by finite element method, rapid convergence and high accuracy are demonstrated. Furthermore, effects of elastic boundary conditions and rings are discussed. Results reveal that mode shapes of shells are significantly affected by rings with T cross-section, and in-plane and out-plane deformations of the web of rings cannot be neglected, especially for rings with large height.