Free vibration analysis of coupled conical-cylindrical shells based on the dynamic stiffness method

In this paper, an analytical method to study the free vibration behavior of coupled conical-cylindrical shells is proposed. The combined shells are firstly divided into multiple substructures at the junction between the two shell segments. Then, Flügge shell theory is utilized to describe the motions of the conical and cylindrical segments. Power series and wave functions are used to express the displacement functions of conical segment and cylindrical segment, respectively. By solving the governing partial differential equations, dynamic stiffness matrixes for individual shell segments are established, respectively. Then, the global dynamic stiffness matrix for the whole combined structure is obtained by assembling dynamic stiffness matrixes of individual shell segments in a similar way as FEM. Free vibration responses of the coupled shells are then obtained based on the whole dynamic stiffness matrix. Through comparing vibration results of present method with ones from open literature and that calculated by FEM for the coupled shells, rapid convergence, wide application and high accuracy of present analytical method are demonstrated. Meanwhile, the influences of different model parameters on the free vibration responses of the coupled shells are investigated in detail.