Responses of partially immersed elastic structures using a symmetric formulation for coupled boundary element and finite element methods

Abstract

Using a coupled BEM/FEM, this work describes a numerical method to compute the response and acoustic radiation for structures partially immersed in fluid. The structures and their responses are assumed to be symmetric about a symmetric plane. A symmetric complex matrix derived from the BEM and a reciprocal principle for surface acoustics is also used to represent the acoustic loading against the structures. In addition, selecting a proper Green's function based on image source method satisfies the boundary conditions of pressure release on the fluid surface and null normal velocity on the symmetric plane. Moreover, a boundary integral equation emerges when the field point approaches the structural surface where the normal derivative of the Green's function over partial, infinitesimal spheres is evaluated. These limiting values depend on locations of the field point on the surface. Owing to the symmetry of the acoustic loading matrix, the matrix for the coupled BEM/FEM is a banded, symmetric one, thereby allowing us to employ a variable banded storage method and invert of the matrix. Doing so markedly increases computational efficiency. Furthermore, an analytical solution of a spherical thin shell with the lower semi-sphere immersed in water is carried out by characteristic function expansions for shell equation and acoustic loading. These analytical solutions compare with the results obtained from the proposed numerical method. A good correlation for low frequencies is obtained and minor discrepancies are observed with an increasing frequency.