TY - JOUR

T1 - A topology optimization of open acoustic waveguides based on a scattering matrix method

AU - Matsushima, Kei

AU - Isakari, Hiroshi

AU - Takahashi, Toru

AU - Matsumoto, Toshiro

N1 - Funding Information:
The authors would like to acknowledge anonymous referees for their valuable comments. This work was supported by JSPS KAKENHI Grant Numbers JP19J21766 and JP19H00740 .
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/8

Y1 - 2022/8

N2 - 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.

AB - 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.

KW - Acoustic waveguide

KW - Bound state in the continuum

KW - Boundary element method

KW - Scattering matrix

KW - Topology optimization

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U2 - 10.1016/j.wavemoti.2022.102987

DO - 10.1016/j.wavemoti.2022.102987

M3 - Article

AN - SCOPUS:85133866013

VL - 113

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

M1 - 102987

ER -