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.

翻译：本文聚焦于瞬态振动声学问题的形状与拓扑优化。主要贡献在于提出一种针对工业领域常关注的复杂信号宽带频率范围的瞬态问题优化框架。该工作采用时域方法实现频域内的宽带优化，具体通过在时域响应上应用快速傅里叶变换（FFT）算法获取系统频响函数，进而在频域定义目标函数。研究采用参数化水平集方法隐式描述几何结构，其中零水平面表征声学域与结构域的界面。通过引入特殊积分方案精确捕捉界面特征的剪切单元方法，在固定背景网格上实现几何表征，从而避免每次设计更新时的网格重构，获得强耦合振动声学系统的高精度解。本文采用基于梯度的优化策略，利用离散伴随法计算目标函数与约束函数的灵敏度，并详细阐述了包含FFT运算（用于频域目标函数定义）的一致性灵敏度计算过程。最后，将该框架应用于多种振动声学滤波器设计，并通过商用有限元软件的稳态时谐公式验证了优化结果。