On the Vibration of an Underwater Shell with Interior Sub-Structures: Modeling and Power Flow Analysis

PurposeEvaluating the vibration of underwater cylindrical shells with internal structures accurately and quickly is very important in the engineering design of underwater vehicles. Conventional finite element analyses will face problems such as extended time consumption and large storage capacity. This paper first proposes a fast calculation scheme based on the assumed mode method for modeling a pump-raft-shell coupled system with a static fluid outside the shell.MethodThe complex structure is first divided into four substructures connected by vibration isolator springs. The free vibration modes of the four substructures are calculated separately by commercial software. The second Lagrange equation establishes the dynamics equations of the coupled structures. Then, the fluid outside the shell is considered as the fifth subsystem, and its influence on the shell is considered as the added fluid mass. Comparison with the finite element method shows that the present method has the advantages of high computing efficiency and accuracy. Finally, the above-developed model and the four-terminal parametric method are combined to study the power flow transfer in the system.Resultsthe present modeling method can effectively be applied to the complex structure response calculation. The power flow level difference varies widely in different frequency bands. Generally, the power flow level difference is symmetric, and the phase difference between the two excitation forces is 180 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${180<^> \circ }$$\end{document}.ConclusionThe results show that the method proposed is highly computationally efficient when calculating cases where the shell is submerged in water; and combined with corresponding optimization methods, it can potentially optimize the design of isolation springs.