The focus of this article is on shape and topology optimization of transient vibroacoustic problems. The main contribution is a transient problem formulation that enables optimization over wide ranges of frequencies with complex signals, which are often of interest in industry. The work employs time domain methods to realize wide band optimization in the frequency domain. To this end, the objective function is defined in frequency domain where the frequency response of the system is obtained through a fast Fourier transform (FFT) algorithm on the transient response of the system. The work utilizes a parametric level set approach to implicitly define the geometry in which the zero level describes the interface between acoustic and structural domains. A cut element method is used to capture the geometry on a fixed background mesh through utilization of a special integration scheme that accurately resolves the interface. This allows for accurate solutions to strongly coupled vibroacoustic systems without having to re-mesh at each design update. The present work relies on efficient gradient based optimizers where the discrete adjoint method is used to calculate the sensitivities of objective and constraint functions. A thorough explanation of the consistent sensitivity calculation is given involving the FFT operation needed to define the objective function in frequency domain. Finally, the developed framework is applied to various vibroacoustic filter designs and the optimization results are verified using commercial finite element software with a steady state time-harmonic formulation.

中文翻译：

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使用切割元件进行宽带滤波器设计的瞬态振动声学问题的拓扑优化

本文的重点是瞬态振动声学问题的形状和拓扑优化。主要贡献是瞬态问题公式，可以在复杂信号的广泛频率范围内进行优化，这在工业界通常是很有趣的。该工作采用时域方法实现频域宽带优化。为此，在频域中定义目标函数，通过对系统瞬态响应进行快速傅里叶变换（FFT）算法来获得系统的频率响应。这项工作利用参数化水平集方法来隐式定义几何结构，其中零水平描述了声学域和结构域之间的界面。切割元素方法用于通过利用精确解析界面的特殊集成方案来捕获固定背景网格上的几何形状。这样可以为强耦合振动声学系统提供准确的解决方案，而无需在每次设计更新时重新划分网格。目前的工作依赖于基于高效梯度的优化器，其中离散伴随方法用于计算目标函数和约束函数的敏感性。给出了一致灵敏度计算的彻底解释，涉及定义频域目标函数所需的 FFT 运算。最后，将开发的框架应用于各种振动声学滤波器设计，并使用商用有限元软件和稳态时谐公式验证优化结果。