Abstract
In this paper we study the fundamental and higher-order modes propagation in a cylindrical acoustic duct with a multi-perforated liner section. This study relies on an established approximate model that is mathematically verified by a multiscale analysis and that takes the presence of the liner into account through transmission conditions. We simulate the reflection and transmission behaviour by an hp-adaptive finite element method that effectively resolves the solution in presence of strong singularities at the rim of the duct. Moreover, we introduce a new mode matching method based on the complete mode decomposition that depends in the liner section on the Rayleigh conductivity. It turns out that the mode matching method achieves similar accuracies with all propagating and just a number of evanescent modes.
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Acknowledgements
The authors gratefully acknowledge the financial support from the Einstein Foundation Berlin (grant number IPF-2011-98) and the research center MATHEON through the Einstein Center for Mathematics Berlin (project MI-2) and are thankful to the fruitful exchange with the DLR Berlin.
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Semin, A., Thöns-Zueva, A., Schmidt, K. (2017). Simulation of Reflection and Transmission Properties of Multiperforated Acoustic Liners. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_9
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DOI: https://doi.org/10.1007/978-3-319-63082-3_9
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