TY - JOUR

T1 - A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation

AU - Honshuku, Yuta

AU - Isakari, Hiroshi

N1 - Publisher Copyright:
© 2022 Elsevier Inc.

PY - 2022/10

Y1 - 2022/10

N2 - We propose a topology optimisation of acoustic devices that work in a certain bandwidth. To achieve this, we define the objective function as the frequency-averaged sound intensity at given observation points, which is represented by a frequency integral over a given frequency band. It is, however, prohibitively expensive to evaluate such an integral naively by a quadrature. We thus estimate the frequency response by the Padé approximation and integrate the approximated function to obtain the objective function. The corresponding topological derivative is derived with the help of the adjoint variable method and chain rule. It is shown that the objective as well as its sensitivity can be evaluated semi-analytically. We present efficient numerical procedures to compute them and incorporate them into a topology optimisation based on the level-set method. We confirm the validity and effectiveness of the present method through some numerical examples.

AB - We propose a topology optimisation of acoustic devices that work in a certain bandwidth. To achieve this, we define the objective function as the frequency-averaged sound intensity at given observation points, which is represented by a frequency integral over a given frequency band. It is, however, prohibitively expensive to evaluate such an integral naively by a quadrature. We thus estimate the frequency response by the Padé approximation and integrate the approximated function to obtain the objective function. The corresponding topological derivative is derived with the help of the adjoint variable method and chain rule. It is shown that the objective as well as its sensitivity can be evaluated semi-analytically. We present efficient numerical procedures to compute them and incorporate them into a topology optimisation based on the level-set method. We confirm the validity and effectiveness of the present method through some numerical examples.

KW - Padé approximation

KW - acoustic device

KW - boundary element method

KW - fast frequency sweep

KW - topological derivative

KW - topology optimisation

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U2 - 10.1016/j.apm.2022.06.020

DO - 10.1016/j.apm.2022.06.020

M3 - Article

AN - SCOPUS:85132788264

SN - 0307-904X

VL - 110

SP - 819

EP - 840

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -