Abstract Topology optimization of dynamic acoustic–mechanical structures is challenging due to the interaction between the acoustic and structural domains and artificial localized vibration modes of structures. This paper presents a floating projection topology optimization (FPTO) method based on the mixed displacement/pressure (u/p) finite element formulation and the ersatz material model. The former is able to release the need for tracking the interface boundaries explicitly between the structural and acoustic domains during the optimization process. The ersatz material model enables us to entirely avoid artificial localized vibration modes caused by the extremely high ratio between mass and stiffness. The floating projection simulates the original 0/1 constraints, and it gradually pushes the design variables toward 0 or 1 at the desired level so that the optimized element-based design can be accurately represented by a smooth design. Some 2D and 3D numerical examples, including minimizing sound pressure at the designated domain, restraining structural vibration, and maximizing sound transmission loss, are presented to demonstrate the effectiveness of the proposed topology optimization algorithm. The optimized solutions achieve the consistency of the objective function between the element-based design using the mixed formulation and the smooth design using the segregated formulation. The study suggests that the FPTO method using the ersatz material model is a promising approach for optimizing dynamic acoustic-mechanical structures.

中文翻译：

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使用ersatz材料模型的动态声学-机械结构的拓扑优化

摘要 由于声学域和结构域之间的相互作用以及结构的人工局部振动模式，动态声学-机械结构的拓扑优化具有挑战性。本文提出了一种基于混合位移/压力 (u/p) 有限元公式和人造材料模型的浮动投影拓扑优化 (FPTO) 方法。前者能够消除在优化过程中明确跟踪结构域和声学域之间的界面边界的需要。人造材料模型使我们能够完全避免由质量和刚度之间极高的比率引起的人工局部振动模式。浮动投影模拟了原始的 0/1 约束，并逐渐将设计变量推向 0 或 1 在所需的水平，以便优化的基于元素的设计可以通过平滑的设计准确地表示。提供了一些 2D 和 3D 数值示例，包括最小化指定域的声压、抑制结构振动和最大化声音传输损失，以证明所提出的拓扑优化算法的有效性。优化后的解决方案实现了使用混合公式的基于单元的设计和使用分离公式的平滑设计之间目标函数的一致性。该研究表明，使用 ersatz 材料模型的 FPTO 方法是优化动态声学机械结构的一种很有前途的方法。