Natural Frequencies of Submerged Structures Using an Efficient Calculation of the Added Mass Matrix in the Boundary Element Method

Abstract

This work presents an efficient way to calculate the added mass matrix, which allows solving for natural frequencies and modes of solids vibrating in an inviscid and infinite fluid. The finite element method (FEM) is used to compute the vibration spectrum of a dry structure, then the boundary element method (BEM) is applied to compute the pressure modes needed to determine the added mass matrix that represents the fluid. The BEM requires numerical integration which results in a large computational cost. In this work, a reduction of the computational cost was achieved by computing the values of the pressure modes with the required numerical integration using a coarse BEM mesh, and then, interpolation was used to compute the pressure modes at the nodes of a fine FEM mesh. The added mass matrix was then computed and added to the original mass matrix of the generalized eigenvalue problem to determine the wetted natural frequencies. Computational cost was minimized using a reduced eigenvalue problem of size equal to the requested number of natural frequencies. The results show that the error of the natural frequencies using the procedure in this work is between 2% and 5% with 87% reduction of the computational time. The motivation of this work is to study the vibration of marine mammals' ear bones.