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arXiv · 2201.09533

A topology optimization of open acoustic waveguides based on a scattering matrix method

Kei Matsushima·Hiroshi Isakari·Toru Takahashi·Toshiro Matsumoto
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Abstract

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.

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Kei Matsushima, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto. 2022-07-07. A topology optimization of open acoustic waveguides based on a scattering matrix method. https://doi.org/10.1016/j.wavemoti.2022.102987

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