Exact solutions for vibration of stepped circular cylindrical shells

Abstract

Based on the Flügge thin shell theory, this paper presents exact solutions for the vibration of circular cylindrical shells with step-wise thickness variations in the axial direction. The shell is sub-divided into multiple segments at the locations of thickness variations. The state-space technique is adopted to derive the homogenous differential equations for a shell segment and domain decomposition method is employed to impose the equilibrium and compatibility requirements along the interfaces of the shell segments. To ensure the correctness of the present results, comparisons are made with one paper available in the open literature based on the Donnell–Mushtari theory. Shells with various combinations of end boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thickness ratios, locations of step-wise thickness variations and step thickness ratios on the natural frequencies and mode shapes are examined. The exact vibration results can serve as important benchmark values for researchers to validate their numerical methods for such circular cylindrical shells.