Dynamic analysis of stepped cylindrical shells with internal bulkheads utilizing characteristic orthogonal polynomials

This study investigates the dynamic properties of stepped cylindrical shells with internal bulkheads. A numerical analysis framework is formulated utilizing the Jacobi polynomials-Ritz method. The construction of the theoretical model incorporates a domain decomposition technique, virtual spring method, and the shear deformation theory, with the introduction of the characteristic orthogonal polynomials to delineate displacement functions. Both the free and forced vibrational behaviors of the structure are obtained by using the Ritz method. Moreover, the time-domain vibration response of the structure is ascertained utilizing the Newmark-β integral approach. This study offers a detailed examination of the influence exerted by factors including spring stiffness, truncation number, and the Jacobi parameter on the convergence of the presented method. The accuracy of the current approach is verified by juxtaposing its results with those derived from the finite element method. Additionally, the investigation explores the dynamic features of the stepped structure subject to different construction parameters, boundary conditions, and configurations of internal bulkheads, as demonstrated through a comprehensive set of numerical examples.