Fluid structure interaction and admittance boundary conditions: Setup of an analytical example

Often, acoustic simulation techniques suffer from errors of the computational model and its parameters. Quantification of the boundary condition is a crucial point for simulations. In particular, the boundary admittance is often unknown and hard to quantify. This article demonstrates how to reduce a fluid-structure interaction model to a pure fluid model with local or nonlocal admittance boundary conditions. Starting point is a BEM formulation for the fluid and a FEM formulation for the structure. An admittance matrix is derived from this formulation. Then, the multidimensional BEMFEM formulation is adjusted to a one-dimensional example, a duct with structural elements at both ends. Two configurations are investigated, one with local admittance boundary conditions and one with nonlocal admittance boundary conditions which result in a diagonal and in a fully populated admittance matrix, respectively.