Vibroacoustic Simulations of Acoustic Damping Materials Using the Finite Cell Method

  • Radtke, Lars (Hamburg University of Technology)
  • Düster, Alexander (Hamburg University of Technology)
  • Marter, Paul (Otto von Guericke University Magdeburg)
  • Duvigneau, Fabian (Otto von Guericke University Magdeburg)
  • Juhre, Daniel (Otto von Guericke University Magdeburg)

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Acoustic damping materials such as foams are typically characterized by a complex micro-structure. Standard simulation approaches are based on a homogenized model in order to avoid the accordingly complex mesh generation. In order to predict the acoustic behavior of foams more accurately, the micro-structure has to be resolved and the interaction between the foam structure and the fluid (air) inside the pores has to be taken into account. The finite cell method (FCM) [1] combines a ficticious domain approach with high-order finite elements and special quadrature rules and was already successfully applied to structural analyses of metal foams [2]. We extend the FCM in order to realize explicit dynamic analyses of coupled fluid-structure interaction (FSI) problems consisting of a (visco-) elastic structure and an acoustic fluid. Both sub-problems are solved using a separate FCM discretization and the interaction is realized using a Neumann-Neumann coupling. The combined system is solved monolithically. This modeling approach comes along with several challenges associated to the ficitcious domain approach in general. As previously observed in other works, finite cells that have only little support in the physical domain may lead to very small critical time step sizes [3]. Further, standard lumping techniques that yield a diagonal mass matrix -- as desired especially in the context of explicit dynamic analyses -- cannot be applied directly [4]. In our presentation, we address these challenges and suggest remedies for the related issues, which are investigated based on simple test problems. This yields a fully automatic simulation pipeline that is used to predict the behavior of an exemplary acoustic foam. The results are verified using a commercial software. The micro-structure of the foam is obtained using computed tomography (CT) scans, which constitute the main input to the pipeline. [1] Parvizian, J. and Düster, A. and Rank, E. Computational Mechanics (2007) 41:121–133. [2] Heinze, S. and Joulaian, M. and Düster, A. Computers & Mathematics with Applications (2015) 70:1501–1517. [3] Meßmer, M. and Teschemacher, T. and Leidinger, L. and Wüchner, R. and Bletzinger, K.U. Computer Methods in Applied Mechanics and Engineering (2022) 400:115584. [4] Joulaian, M. and Duczek, S. and Gabbert, U. and Düster, A. Computational Mechanics (2014) 54:661–675.