Discrete Flow Mapping in coupled two and three dimensional domains: a global interface problem

Abstract

Discrete Flow Mapping (DFM) was recently introduced as a mesh-based high frequency method for modelling structure-borne sound in complex structures comprised of two-dimensional shell and plate subsystems. The method has now been extended to model three-dimensional meshed structures, giving a wider range of applicability and also naturally leading to the question of how to couple the two- and three-dimensional substructures. We consider this problem for the case of a three dimensional interior fluid domain, enclosed by a two dimensional shell/plate system. In Discrete Flow Mapping, the transport of vibrational energy between substructures is typically described via a local interface treatment where wave theory is employed to generate reflection/transmission and mode coupling coefficients. In our case the entire two-dimensional substructure forms a global interface whose radiating properties will depend on both the geometry and the frequency. In this paper we discuss how such a model may be formulated, including both structural radiation and the back-loading of the fluid pressure on the structure.