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

Yuta Honshuku, Hiroshi Isakari

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)819-840
Number of pages22
JournalApplied Mathematical Modelling
Volume110
DOIs
Publication statusPublished - 2022 Oct

Keywords

  • acoustic device
  • boundary element method
  • fast frequency sweep
  • Padé approximation
  • topological derivative
  • topology optimisation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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