Dynamic Stiffness Formulation for Free Vibration Analysis of Rotating Cross-Ply Laminated Combined Elliptical-Cylindrical-conical Shell

The dynamic stiffness method (DSM) is presented to carry out the vibration analysis of the rotating cross-ply laminated elliptical-cylindrical-conical combined shell considering Coriolis and centrifugal accelerations as well as the hoop tension. The combined shell is composed of three primary substructures: elliptical shell, cylindrical shell and conical shell. To ensure the stability of numerical calculations, individual substructures are further divided into a number of the appropriate shell segments. Based on the first-order shear deformation theory (FSDT) and the Hamilton's principle, a unified dynamic analytical model for rotating cross-ply laminated shell of revolution is established. According to the relationship between the state vector and its derivative, the symmetric dynamic stiffness matrix and the antisymmetric dynamic stiffness matrix of each shell segment are derived. Then, the dynamic stiffness matrix of each segment in the substructure is assembled into the overall matrix by implementing the matrix assembly procedure. To verify the validity of the current method, the dynamic stiffness solutions are compared with those from the available literature and FEMABAQUS. Also, the effects of boundary constraints, geometric parameters, angular velocity, etc. on the dynamic behaviors of the cross-ply laminated combined shell are investigated in detail.