Keywords: added mass, wet modes, natural frequencies.

This paper presents an efficient way to calculate the added mass matrix used to determine the natural frequencies and modes of solids vibrating in an inviscid, incompressible infinite fluid. This work uses the procedure presented by Antoniadis and Kanarachos [1]. Antoniadis and Kanarachos presented a general methodology to decouple the structure and fluid domains to solve for modal analysis. They used the common procedure based on the implementation of the finite element method (FEM) to compute the basis vectors of the structure and the corresponding 'mass' and 'stiffness' matrix terms of the 'dry' structure, while the boundary element method (BEM) was used to solve a set of potential (Laplacian) problems for the fluid, using the previous basis vectors in the place of the structural displacement at the normal pressure derivative (Neumann) boundary condition on the fluid-structure interface. The BEM does not scale well and results in a 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. In acoustic analysis using the FEM it is necessary to include a large amount of degrees of freedom to obtain accurate results. In addition, it is often required to compute the response of a structure for stimuli at different frequencies. For these reasons, a method to reduce the cost of the simulations is highly desirable.

Results are presented for a clamped plate and a free plate. Analytical and experimental results from the literature, as well as results using the commercial code COMSOL are used for comparison. Results using the present approach with fine meshes and a direct computation of the pressure modes implemented in the free code FAESOR closely agree to those used for comparison. Results interpolating the pressure modes of a coarse mesh to obtain the pressure modes of a fine mesh, give good approximations of the natural frequencies of a submerged structure. Although the procedure using interpolation to obtain the pressure modes is not as accurate as the procedure that computes the pressure modes directly at the location of each node, it significantly reduces the computation cost of the pressure modes.

1

I. Antoniadis, A. Kanarachos, "A decoupling procedure for the modal analysis of structures in contact with incompressible fluids", Communications in Applied Numerical Methods, 3, 507-517, 1987. doi:10.1002/cnm.1630030611

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