This article presents a method for generalized shape optimization of time-harmonic vibroacoustic problems. The modeling approach utilizes an immersed boundary cut element method in conjunction with a level set representation of the geometry. The cut element method utilizes a fixed background mesh, a dimensionless contrast parameter and an integration scheme to realize complex geometries and obtain accurate physical solutions to the governing problem. The design parameterization is obtained using a nodal level set description, directly linked to the mathematical design variables, and the gradients of the objective and the constraints are obtained with the discrete adjoint approach. The framework is applied to the optimization of three 2D examples. A study on the effect of initial guess for the proposed optimization procedure is presented on a benchmark example of the design of an acoustic partitioner. Further optimization examples include design of a wave splitter to realize prescribed frequency dependent directivity for emitted acoustic waves and a suspension structure design to improve the performance of a simplified 2D model of a hearing instrument. The results demonstrate that, even though the final topology is strongly dictated by the initial design, modifying the shape allows for a significant improvement of the system behavior.

本文提出了一种时谐振动声学问题的广义形状优化方法。建模方法利用浸入边界切割元素方法结合几何的水平集表示。切割元法利用固定的背景网格、无量纲的对比度参数和积分方案来实现复杂的几何形状并获得控制问题的精确物理解。设计参数化是使用节点水平集描述获得的，直接链接到数学设计变量，目标和约束的梯度是通过离散伴随方法获得的。该框架应用于三个二维示例的优化。在声学分区器设计的基准示例中，研究了初始猜测对所提出的优化程序的影响。进一步的优化示例包括设计分波器以实现发射声波的指定频率相关方向性，以及悬浮结构设计以提高助听器简化 2D 模型的性能。结果表明，即使最终拓扑由初始设计强烈决定，修改形状也可以显着改善系统行为。进一步的优化示例包括设计分波器以实现发射声波的指定频率相关方向性，以及悬浮结构设计以提高助听器简化 2D 模型的性能。结果表明，即使最终拓扑由初始设计强烈决定，修改形状也可以显着改善系统行为。进一步的优化示例包括设计分波器以实现发射声波的指定频率相关方向性，以及悬浮结构设计以提高助听器简化 2D 模型的性能。结果表明，即使最终拓扑由初始设计强烈决定，修改形状也可以显着改善系统行为。