Vibration analysis by impedance synthesis method of three-dimensional piping connected to a large circular cylindrical shell

Pipe systems connected to large cylindrical shells are common structures in submarines and airplanes. The vibration behavior of such structures has attracted not much attention. Based on the kinematic compatibility and force equilibrium conditions at the connection points, the main aspect of this work is to establish a dynamic model of a thin cylindrical shell coupled with a pipe system by using the impedance synthesis method. The structure is divided into a piping substructure and a cylindrical-shell substructure. Impedance formulations of the pipes and the large cylinder are based on Timoshenko beam theory and Flugge shell theory, respectively. Natural frequencies and dynamic responses are obtained by the proposed method and validated against analytical results and finite-element (FEM) simulations. The vibration spectrum of one coupled test structure was analyzed. The so-called cross impedance has a significant effect on the vibration of the coupled structure when the stiffness of the connection points is large compared to that of pipes and shell. It is shown that the impedance synthesis method is an efficient and fast (compared to FEM) tool.