Vibro-Acoustic Simulations of Ships by Coupled Fast BE-FE Approaches

The vibration behavior of ships is noticeably influenced by the surrounding water, which represents a fluid of high density. In this case, the feedback of the fluid pressure onto the structure cannot be neglected and a strong coupling scheme between the fluid domain and the structural domain is necessary. In this work, fast boundary element methods are used to model the semi-infinite fluid domain with the free water surface. Two approaches are compared: A symmetric mixed formulation is applied where a part of the water surface is discretized. The second approach is a formulation with a special half-space fundamental solution, which allows the exact representation of the Dirichlet boundary condition on the free water surface without its discretization. Furthermore, the influence of the compressibility of the water is investigated by comparing the solutions of the Helmholtz and the Laplace equation. The ship itself is modeled with the finite element method. A binary interface to the commercial finite element package ANSYS is used to import the mass matrix and the stiffness matrix. The coupled problems are formulated using Schur complements. To solve the resulting system of equations, a combination of a direct solver for the finite element matrix and a preconditioned GMRES for the overall Schur complement is chosen. The applicability of the approach is demonstrated using a realistic model problem. Nomenclature Ωs, Ωa structural domain, acoustic domain V , D single layer potential, hypersingular operator Γs, ΓI structural boundary, coupling interface K, K ′ double layer potential and its adjoint ΓH half-space boundary K m BE, C m BE Galerkin matrices of mixed formulation ts, tf tractions on Γs and ΓI K h BE, C h BE Galerkin matrices of half-space formulation ̺s, λ, μ structural density, Lamé constants KFE dynamic stiffness matrix n unit normal direction of the fluid domain CFE coupling matrix u structural displacements T q transformation matrix cf , ̺f speed of sound and density of the fluid S Schur complement p, q acoustic pressure and flux cd near-field parameter p̄, q̄ prescribed pressure and flux ce expansion length parameter p̃, q̃ unknown pressure and flux L expansion length f excitation frequency h (1) l Hankel functions ω, κ wave number, circular wave number Pl Legendre polynomials P (x, y) fundamental solution s far-field direction P (x, y) half-space fundamental solution D distance vector between clusters