A refined mode superposition method for dynamical responses of an underwater cylindrical shell with substructures

To overcome the difficulties of time-consuming and inefficient in the response calculations of the submerged cylindrical shell with internal substructures, this paper firstly presents a refined mode superposition method. In view of the necessity and difficulties of directly and quickly obtaining the frequencies and modes of structures submerged in fluid (named the wet modes), the wet modes are expanded by the modes in vacuum (dry modes) and solved by the energy method. The added kinetic energy of the fluid is calculated via boundary integration, and the Lagrange equations of the second kind is applied to the fluid-structure coupling equations. Then the wet modes are solved by eigenvalue calculation and the modal mass and stiffness of each order wet mode are obtained. Finally, they are used for establishing a mode superposition approach for response calculations. The accuracy of the present method is verified by ANSYS software. In this method, all the required data are obtained from the structural analysis and the traditional complicated fluid force modeling is no longer required. Thus it has the advantages of high computational efficiency and applicability. Compared to the traditional semi-analytic model, this modeling methodology has broad application potential for vibration problems of complex underwater structures since the structural dry modes can be solved efficiently by commercial software. It also has practical value as a theoretical reference for developing mode-superposition-based calculations for fluid-structure problems using commercial software.