On designing wave devices, perturbation in excitation frequency might give rise to serious degradation in the device performance. To address this issue, in our previous research, a robust topology optimisation (RTO) for acoustically rigid structures has been proposed. In the RTO, the angular frequency of the incident wave is assumed to be a stochastic variable subject to the normal distribution, and the uncertainty in the response is modelled using high-order Taylor's expansion. Our high-order RTO has successfully broadened the working bandwidth of acoustic devices. In this study, we extend our RTO to design viscoelastic structures involving acoustic–elastodynamic coupled waves in two dimensions. This enables us to deal with materials having more realistic acoustic properties than the rigid one. However, the computation of high-order derivatives for the coupled problem can result in low efficiency, which becomes the main difficulty in realising desirable optimisation for large scale problems. We thus propose an acceleration of our boundary element method (BEM) by employing the H-matrix method and the fast multipole method (FMM) and install the new BEM into the RTO. The proposed RTO is numerically exemplified by several acoustic designs. The results show that the proposed method can find the shape of wideband acoustic devices within a feasible computational time.
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