Finite-Elemente-Methoden, Lösungsalgorithmen und Werkzeuge für die akustische Simulationstechnik

• Finite element methods, algorithms and tools for acoustic simulations

Franck, Andreas; Vorländer, Michael (Thesis advisor)

Berlin : Logos (2009)
Dissertation / PhD Thesis

In: Aachener Beiträge zur technischen Akustik 9
Page(s)/Article-Nr.: VI, 155 S. : Ill., graph. Darst.

Zugl.: Aachen, Techn. Hochsch., Diss., 2008

Abstract

This work presents the development of finite element methods, efficient solution algorithms and application tools for acoustic simulation. Its objective was to create an open, customizable collection of simulation tools with broad applicability, to be able to solve typical acoustic simulation problems with good accuracy and reasonable modeling effort. With an implementation of the FEM for fluid media and an equivalent fluid approach for porous absorber structures, a sound propagation model for airborne sound is implemented. To enable the solution of sound transmission problems through solid structures and the analysis of structure-borne sound, finite element methods for solids and shear flexible plates have been implemented; a full coupling model accounts for the structural loading due to sound pressure and the sound radiation by vibrating structural surfaces. This coupling enables the correct calculation of the effect of non-locally reacting wall structures and the sound transmission through complex panel systems. The methods have been verified regarding their precision and their application limits through a number of benchmark problems. The FEM modeling of complex acoustic systems leads to a system of equations with a large number of degrees of freedom. This system needs to be solved using efficient numerical methods; preconditioned iterative solution methods allow the efficient solution without the need to decompose a large bandwidth system matrix. To apply the developed FEM methods to different acoustic problems, a number of specialized simulation tools have been developed. Methods for the calculation of far field radiation by an extended post-processing of FEM results have been implemented, acoustic impedance models were introduced and verified for the simulation of layered wall structures. A further tool enables the coupled simulation with electromechanical network models. Finally, the tools and methods were verified in two practical application examples from room and building acoustics. The simulation of the low-frequency room acoustics of a recording studio, compared with actual measurement results from the studio, demonstrates the opportunities for numerical acoustics simulations in very complex acoustic environments. A partition wall problem from building acoustics demonstrates all typical effects to be expected from the analysis of both bend-proof and flexible partitions.