Coupling impedance boundary conditions for absorptive structures with spectral finite elements in room acoustical simulations

Models for Fluid Structure Interaction (FSI) in room acoustical calculations are used in many different fields of engineering like automotive industry or civil engineering. In order to obtain the sound field within an acoustic cavity, which is covered by absorptive boundary structures, with its spatial distribution, very often techniques based on Finite Element formulations are used instead of energy methods. In order to reduce the number of degrees of freedom and therefore the numerical effort, a model reduction method, based on a Component Mode Synthesis (CMS), is presented in this article. Macrostructures are assembled out of single substructures applying shape functions at the interfaces. These substructures contain acoustical design elements, like absorbers or resonators. They are calculated separately in the frame of the CMS approach. The acoustic fluid is modeled with the Spectral Finite Element Method (SEM) and coupled with plate-like compound absorbers at interfaces via impedances using Hamilton's Principle and a Ritz approach. The porous foam in the absorber is modeled with the Theory of Porous Media (TPM) and the impedances are calculated with the help of the Integral Transform Method (ITM). The method for coupling two macrostructures is compared with an analytical solution and the model for the porous absorber is validated via measurements. Finally an example for the coupled system is presented.