Modal based model reduction techniques for FSI-problems in room acoustics

In room acoustical simulations energy-methods often are used to predict the sound-field in closed volumes. Those methods are robust for subsystems with high modal density. However, their performance is limited if the spatial resolution of the response is of interest or if complex boundary conditions (e.g. plate resonators or passive absorbers) have to be considered. Numerical methods like the Finite Element Method (FEM) or the Spectral Finite Element Method (SFEM) are used for this task. The order of the polynomials in the SFEM-approach, as well as the number of elements in FEM and the SFEM model, have to be adapted to the corresponding wave length in the frequency range of interest. Therefore, the number of unknowns increases with higher frequencies. Model reduction methods (e.g. the Craig-Bampton Method) are used to reduce the numerical size of the coupled problem, applying attachment modes at the interfaces. Because of the fact, that the coupling has to be carried out over the whole area of the interface, a large number of nodal attachment modes has to be introduced. Thus these reduction methods become inefficient for these kinds of problems. In the paper the classic Craig-Bampton method is compared with a modal based approach, where the modeshapes of the substructures are used to calculate attachment modes for the coupling and the unknowns therefore are no longer linked with the number of nodes at the interface. A modification of this method for the coupling of complex structures within the room (not only at the boundaries) is presented and an outlook concerning the implementation in a model for acoustic cavities considering absorptive boundary conditions is given.      «

In room acoustical simulations energy-methods often are used to predict the sound-field in closed volumes. Those methods are robust for subsystems with high modal density. However, their performance is limited if the spatial resolution of the response is of interest or if complex boundary conditions (e.g. plate resonators or passive absorbers) have to be considered. Numerical methods like the Finite Element Method (FEM) or the Spectral Finite Element Method (SFEM) are used for this task. The ord...     »