A dynamic stiffness formulation for the vibration analysis of rotating cross-ply laminated coupled conical-cylindrical-conical shells

In this paper, a dynamic stiffness formulation is reported to analyze the free vibration characteristics of a rotating cross-ply laminated coupled conical-cylindrical-conical shell. In order to ensure the stability of the numerical results, the whole system is firstly divided into substructures, and each substructure is divided into several segments. The theoretical formulation of the rotating shell segment is derived by the first-order shear deformation theory and Hamilton's principle. The effects of centrifugal force and Coriolis acceleration on the initial hoop tension are considered in the formulation. The dynamic stiffness matrix of the shell segment is derived from the relationship between the state vector and its derivative, where the state vector consists of the resultant force and displacement components of the shell segment. The dynamic stiffness matrix of the whole system is assembled by the displacement coordination relationship. After the number of segments is determined by the convergence analysis, it is compared with the results of the existing literature and finite element software to ensure the accuracy of the dynamic stiffness formulation. Based on this, the effects of rotational speed, geometry and boundary conditions on the structure are studied.