A hybrid analytic–numerical formulation for the vibration analysis of a cylindrical shell coupled with an internal flexural floor structure

A hybrid analytic–numerical formulation is developed to study the vibration behaviors of a cylindrical shell coupled with an internal flexural floor structure. The full structure is divided into a cylindrical shell, axisymmetric annular plates and a non-axisymmetric floor structure. The cylindrical shell and annular plates are analyzed by the analytic dynamic stiffness method (DSM) while the floor is modeled by the finite element method (FEM), so the line connections between the cylindrical shell and interior floor degrade into discrete point connections. At each coupling point, virtual springs are used to couple the cylindrical shell and interior floor, and coupling conditions at six Dofs are fully taken into consideration. In DSM, the displacement solutions of the cylindrical shell and annular plate are described by exponential functions and Bessel functions, respectively. In FEM, the dynamic condensation technique is adopted to reduce the model Dofs, while the main dynamic characteristic of the FEM model is preserved as much as possible. To verify the accuracy and effectiveness of present formulation, vibration results calculated by present method are compared with those obtained from FEM and a test experiment. Moreover, the effects of ribs, bulkheads, coupling conditions, boundary conditions of the shell and structural damping on the vibration responses are also investigated.