Coupled Finite and Boundary Element Methods for Vibro-Acoustic Interface Problems

Abstract

As a vibro-acoustic interface model problem we consider a three-dimensional elastic body, e.g., a submarine, which is completely immersed in a full space acoustic region, e.g., water [5]. Other applications that we have in mind are the sound radiation of passenger car bodies, where the acoustic region is bounded, or of partially immersed bodies such as ships, where the acoustic region is a half space [2].In this paper, we consider both a direct simulation of the interface problem by using a symmetric coupled finite and boundary element approach, and an eigenvalue analysis to determine the eigenmodes of the coupled system. The time-harmonic vibrating structure in˝s is modeled by the Navier equations in the frequency domain, while the acoustic fluid in the unbounded exterior domain˝f is described by the Helmholtz equation,In (1), and are the Lamé parameters, % s and % f are the densities of the structure and of the acoustic fluid, respectively, ! is the frequency, and Ä D !=c 2 R is the wave number. Note that˝s

A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver

“…With the reciprocal theorem between p andp in Ω \ Ω ε , and Eqs. (13), (21), (22), (25) and (26), we can evaluate δJ as follows:…”

“…This choice is reasonable since, with our settings, the elastic material is in a bounded domain while the acoustic host matrix is unbounded. Although the acoustic-elastic coupled problem can appropriately be solved by the BEM [18,25], we use the BEM-FEM solver [13] since the solver can naturally be extended to deal with elastic material other than the isotropic one such as anisotropic material and Biot's poroelastic material [6,7]. So far, some fast techniques [14] for the BEM-FEM solver are proposed.…”

Coupled Finite And Boundary Element Methods for Fluid-Solid Interaction Eigenvalue Problems

“…For the coupled formulation of the eigenvalue problem (1) we use a coupled field and boundary integral formulation which was first presented and analyzed in [8] and which was later considered in [14]. The focus in [8] were source problems and therefore the analysis was restricted to positive frequencies.…”

“…Let Re(ω) > 0 and assume that (u, p) ∈ H 1 (Ω S ) × H 1/2 (Γ) is a solution of (13). Further, letp be defined by (14). The assumption ker(D(k)) = {0} implies that we can construct a unique outgoing solutionp ∈ H 1 loc (Ω F ) of the Neumann problem of the Helmholtz equation…”

“…Our formulation of the resonance problem is based on a field equation for the solid and on boundary integral equations for the fluid. This formulation was first proposed in [8] for source problems and later considered in [14]. The analysis of the formulation in [8] is restricted to real frequencies and it is shown that the Fredholm alternative can be applied in the natural energy spaces for the displacement and for the acoustic pressure.…”