A topology optimisation of acoustic devices based on the frequency response estimation with the Pad\'{e} approximation

TL;DR

This paper introduces a topology optimization method for acoustic devices operating over a specific bandwidth, utilizing Padé approximation for efficient frequency response estimation and level-set methods for design optimization.

Contribution

It presents a novel approach combining Padé approximation with topology optimization to efficiently design broadband acoustic devices.

Findings

Efficient semi-analytical evaluation of objective and sensitivities.

Validated numerical examples demonstrating method effectiveness.

Reduced computational cost via frequency response approximation.

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 Pad\'{e} 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 and 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.