A robust topology optimization for enlarging working bandwidth of acoustic devices
A robust topology optimization for enlarging working bandwidth of acoustic devices
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DOI：
10.1002/nme.6637
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发表时间：
2021-02
影响因子：
2.9
通讯作者：
Jincheng Qin;H. Isakari;Kouichi Taji;Toru Takahashi;Toshiro Matsumoto
中科院分区：
文献类型：
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作者：
Jincheng Qin;H. Isakari;Kouichi Taji;Toru Takahashi;Toshiro Matsumoto
我们提出了一种新的强大的拓扑优化设计的声学设备，是有效的宽带声波。在这里，我们定义的目标函数作为一个单一的频率和它的标准偏差（SD）对频率扰动组成的入射波的声学响应的加权和。通过近似SD，假设事件频率遵循正态分布，利用（常规）目标函数的高阶泰勒展开，我们处理显著的频率变化。为了计算这样的近似，我们需要计算状态变量的高阶频率导数。在这里，我们定义它们的积分表示，这使我们能够表征它们，即使当状态变量定义在一个无界域中，通常是波散射问题的情况下。我们进一步表明，基于这个定义，高阶导数可以有效地计算边界元法和自动微分的组合。我们还提出了一个新定义的目标函数的拓扑导数的推导和计算。我们将所有提出的技术安装到基于水平集方法的拓扑优化方法中，以设计宽带声学器件。通过几个算例验证了所提出的拓扑优化方法的正确性和有效性。
We propose a novel robust topology optimization for designing acoustic devices that are effective for broadband sound waves. Here, we define the objective function as the weighted sum of the acoustic response to an incident wave consisting of a single frequency and its standard deviation (SD) against the frequency perturbation. By approximating the SD, under the assumption that the incident frequency follows the normal distribution, with the high‐order Taylor expansion of the (conventional) objective function, we deal with significant frequency variations. To calculate such an approximation, we need to calculate the high‐order frequency derivatives of the state variable. Here, we define them by integral representations, which enables us to characterize them even when the state variable is defined in an unbounded domain as is often the case with wave scattering problems. We further show that, based on this definition, the high‐order derivatives can efficiently be computed by a combination of the boundary element method and automatic differentiation. We also present a derivation and calculation of the topological derivative for the newly defined objective function. We install all the proposed techniques into a topology optimization method based on the level‐set method to design wideband acoustic devices. The validity and effectiveness of the proposed topology optimization are confirmed through several numerical examples.