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.

翻译：我们建议对在一定带宽内起作用的声学装置进行地形优化。 为此, 我们将目标功能定义为特定观测点的频率平均声音强度, 以特定频带的频率组成, 然而, 以一个等宽度来天真地评价这种整体性, 费用太高。 因此, 我们估计了Pad\' {e} 近似值的频率反应, 并结合了近似函数以获得客观功能。 相应的表层衍生物是在联合变量方法和链规则的帮助下产生的。 这表明, 目标及其灵敏度可以进行半分析性评估。 我们提出了高效的数字程序, 来计算它们并将其纳入基于水平定法的地形优化。 我们通过一些数字示例确认当前方法的有效性和有效性。