ITM-Based FSI-Models for Room Acoustical Simulations

Abstract

In many different fields of engineering, like automotive industry or civil engi- neering, room acoustical tasks are of interest. Sound fields have to be predicted in order to design the acoustic cavity by placing acoustic elements like reflectors or absorbers (passive absorbers or plate resonators) into the room for example. Therefore models for the Fluid Structure Interaction (FSI) are used, where passive absorbers or plate resonators can be con- sidered. For simulations of the spatial resolution of the sound field within acoustic cavities very often techniques based on Finite Element formulations are used. 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 applied in this contribution. The advan- tage is related to the fact, that the modal analysis is done only once for the rigid walled cavity, which is modeled with Spectral Finite Elements (SFEM). The cavity boundary condi- tions, e.g. compound absorbers made of homogenous plates and porous foams, are modeled using Integral Transform Methods (ITM). Therefore the differential equations of motion are established for the individual components, where the Lam´ e Equation is used for homogenous and the Theory of Porous Media (TPM) for porous materials. These equations are solved in the wavenumber-frequency domain after applying a Fourier Transformation. The results (wavenumber dependent impedances) for the absorptive structure are coupled with the acous- tic cavity adding interface coupling modes for the fluid and applying Hamilton's principle, considering the velocity of both components to coincide as a constraint at the interface. The method is presented and models of the subsystems, the absorber and the fluid, are shown. Finally examples for the simulation of the coupled structure are presented.