A topology optimization of open acoustic waveguides based on a scattering matrix method
| Title: | A topology optimization of open acoustic waveguides based on a scattering matrix method |
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| Authors: | Matsushima, Kei, Isakari, Hiroshi, Takahashi, Toru, Matsumoto, Toshiro |
| Source: | Wave Motion 113C (2022) 102987 |
| Publication Year: | 2022 |
| Collection: | Computer Science Mathematics Physics (Other) |
| Subject Terms: | Mathematics - Numerical Analysis, Physics - Computational Physics, 49M41, G.1.9, G.1.6, J.2 |
| More Details: | This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai--Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments. Comment: 30 pages, 13 figures |
| Document Type: | Working Paper |
| DOI: | 10.1016/j.wavemoti.2022.102987 |
| Access URL: | http://arxiv.org/abs/2201.09533 |
| Accession Number: | edsarx.2201.09533 |
| Database: | arXiv |
| DOI: | 10.1016/j.wavemoti.2022.102987 |
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