Vibration analysis of double-walled cylindrical shells interconnected with arbitrary connections using a unified semi-analytical method

The vibration characteristics of double-walled cylindrical shells interconnected with arbitrary connections are predicted through a unified semi-analytical method. The motions and displacement fields of inner and outer shells are expressed by Flugge shell theory and wave based method (WBM). To make the present method applicable for arbitrary connections, finite element method (FEM) is adopted to establish their dynamic equations. The coupling with 6 degree of freedoms (DOFs) between the shells and connections are realized using a precise equivalent transformation. Then, a series of artificial springs with 6 DOFs, rather than just 4 DOFs in existing papers, are introduced at each coupling node to achieve general coupling conditions. Through displacement and force continuities between the inner shell, connections and outer shell, the final vibration governing equations are established. Two typical engineering structures, namely double-walled cylindrical shells interconnected by annular plates and splints, are employed to validate the proposed approach. Results show that vibration responses of the shells using the proposed method agree well with the ones presented in literature and calculated through FEM. Furthermore, effects of connecting forms, general coupling and boundary conditions on vibration behaviors are evaluated and several significant phenomena are discovered.