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• We developed a new topology optimisation method to design wide-band acoustic devices. • The method is based on the Padé approximation of acoustic response. • The analytical expression for the frequency integral of the approximated response and its sensitivity is obtained. • Some numerical examples of wide-band acoustic devices are presented. 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. [ABSTRACT FROM AUTHOR]

We propose a numerical method for a topology optimisation of composite elastic metamaterial slabs. We aim to realise some anomalous functionalities such as perfect absorption, wave-mode conversion, and negative refraction by designing the shape and topology of (visco-)elastic inclusions. Instead of manipulating effective material constants, we propose to utilise the far-field characteristics of scattered waves. This allows us to achieve novel functionalities for waves in not only low- but also high-frequency ranges. The design sensitivity corresponding to the far-field characteristics is rigorously derived using the adjoint variable method and incorporated into a level-set–based topology optimisation algorithm. The design sensitivity is computed by the boundary element method with periodic Green's function instead of the standard finite element method to rigorously deal with the radiation of scattered waves without absorbing boundaries. We show some numerical examples to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a structural optimisation method in three-dimensional acoustic–elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic–elastic coupled problems. In this paper, the acoustic–elastic coupled problems are solved by a BEM–FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM–FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method. [ABSTRACT FROM AUTHOR]