Acoustical behavior of poroelastic plates

In many fields of engineering, combinations of several materials have to be used to achieve the required behavior. In particular, the sound insulation of a structure is normally obtained by attaching some porous layers to the solid structure carrying the load. Examples are walls of buildings, the engine hood of a car, or the side wall of an aircraft. In this project, the latter will serve as model problem because it covers all aspects of such a construction. The aim is to simulate the acoustic behavior of a layered plate like structure. Different to a composite plate, here, clearly identifiable layers are considered where the connection between them vary from tight to loose or it is simply an air gap. Hence, not only the plate itself but also the coupling has to be considered. Whereas the porous structure requires the development of a poroelastic plate theory, the other structural elements can be modeled with known techniques. But, the coupling between the single layers has to be rigorously analyzed. Finally, the numerical simulation tool will be validated by experiments. Such a complex problem with the wide area from the development of a poroelastic plate theory versus the simulation of the coupling to the experimental validation cannot be tackled by one applicant. Therefore, a cooperation with Prof. O. v. Estorff, Hamburg University of Technology, has been established and the airborne acoustics as well as all experimental topics and the simulation of the sound radiation will be treated there. The poroelastic plate theory will be developed in Graz and the coupling of the layers by both proposers.

The main purpose of this project was to improve the numerical simulation of the sound transmission through multi-layered panels, which can be composed of different plates, e.g. of elastic, poroelastic, or fibrous material. Very often, also thin air layers occur in the overall panel setup. Applications of such constructions can be found, e.g., in the fuselage of aircrafts. Before the start of the project, numerous models existed which were able to predict well the behavior of elastic plates by both 3-D and 2-D formulations. Since a 2-D model can be discretized in a rather easy way and often has less degrees of freedom, it became the preferred choice for real life applications. An efficient 2-D formulation of poroelastic and fibrous plates, however, did not exist yet. Therefore, within the current project a new formulation of poroelastic plates has been developed. It eliminates the thickness of the plate under investigation by approximating its dynamic behavior with a polynomial series. The same methodology is further used to develop a so-called air-plate formulation, which solves the acoustical problem in a thin layer of fluid. It is noteworthy that the air-plate model is not only valid for air gaps between multi-layered panels, but also for some fibrous plates, since those fibrous materials can be regarded as a fluid with specific acoustical properties. With the help of the newly developed plate models, the sound transmission of multi-layered panels can be completely simulated by plate elements. This means that no matter how many layers are included, each can be modeled with a single layer of 2-D elements. The coupling of the different plates and the construction of efficient solvers have been developed by the partner at TU Hamburg-Harburg. Further, the experimental verification of the model has been done there.