Efficient Calculation of the Added Mass Matrix for Vibration Analysis of Submerged Structures

Abstract

This paper presents an efficient way to calculate the added mass matrix used to solve for the natural frequencies and modes of solids vibrating in an inviscid, incompressible infinite fluid. Finite element method is used to compute the vibration spectrum of just the dry structure, and boundary element method (BEM) is then applied to compute the frequencies and modes of the wetted structure. The BEM does not scale well and results in large computing cost. A reduction of the computational cost to compute the added mass was achieved using a coarse mesh in the BEM and subsequent interpolation to compute the pressure modes at the nodes of a fine mesh from the results of a coarse mesh. Although, damping can also influence the frequencies and modes of the submerged structure, the effects of damping are not taken into account in this work to reduce the cost of the computation time. Excitation of the structure by intermodal coupling is also not taken into account.