Dynamic stiffness formulation for vibration analysis of an open cylindrical shell and its coupling structures based on a generalized superposition method

Abstract

• A dynamic stiffness formulation is provided for open cylindrical shells. • The dynamic stiffness formulation is derived by combining a generalized superposition method with the projection method. • Compared with available ones, the derivation process of the dynamic stiffness matrix is easier in the present formulation and its dimension is also largely reduced. • The present formulation is appropriate for various boundary conditions. • The present formulation is extended to the vibration analysis of coupled shell structures. • Parametric studies are performed on the vibration of coupled shell structures. This paper presents a dynamic stiffness formulation for free vibration analysis of open cylindrical shells and their coupling structures. Based on the Flügge's thin shell theory, the dynamic stiffness matrix of an open cylindrical shell is derived by employing the projection method and a newly developed superposition method, which considers the entire domain of the system as a whole part instead of dividing it into small subdomains in the traditional Gorman's superposition method. By doing this, the derivation process of the dynamic stiffness formulation is much easier and the analytical model has a significantly lower order than the traditional dynamic stiffness formulation. The presented dynamic stiffness formulation is then extended to the vibration analysis of coupled shell structures. To achieve this goal, the coupled shell structures are divided into several sub-shells, and the global dynamic stiffness matrices are assembled according to the geometrical coupled conditions between them. Several typical coupled shell structures are taken as examples and their vibration characteristics are studied by the present formulation. The convergence and accuracy of the present formulation are verified by comparing present results with those obtained by literature and the finite element method (FEM). Parameter studies for the vibration analysis of the coupled shell structures are presented, indicating that the circumference angles, length-to-radius ratios, and thickness-to-radius ratios have significant influences on the dynamic characteristics of the coupled shell structures.