The poroelastic material is often used as a sandwich core due to its lightweight and excellent sound insulation and absorption, and the research revealed that poroelastic materials with macro- or meso-holes could further improve its sound insulation performance. This study proposes a topology optimization approach to design poroelastic cores of sandwich structures for sound insulation. The mixed displacement/pressure (u/p) formulation based on Biot's theory and the ersatz material model are used to overcome the potential difficulties in topology optimization. The floating projection topology optimization method (FPTO) for maximizing sound transmission loss (TL) of sandwich structures filling with poroelastic materials is established based on the floating projection constraint, which simulates 0/1 constraints of the design variables. Some 2D and 3D numerical examples are given to demonstrate the capability and effectiveness of the proposed topology optimization algorithm. The results show that the distribution of the poroelastic material often concentrates at some locations. The traditional sandwich structures often have periodic cores, considering the ease of manufacture and the resistance of uncertain external loads. Therefore, topology optimization of periodic structures for sound insulation is also investigated in this paper. The numerical examples indicate that optimized periodic cores of sandwiches make the poroelastic material to be distributed evenly within the design domain but slightly scarify the sound insulation performance.

多孔弹性材料因其重量轻、隔音吸声性能好而常被用作夹层芯材，研究表明具有大孔或中孔的多孔弹性材料可以进一步提高其隔音性能。本研究提出了一种拓扑优化方法来设计隔声夹层结构的多孔弹性芯。混合排量/压力（u / p) 基于 Biot 理论的公式和替代材料模型用于克服拓扑优化中的潜在困难。基于浮动投影约束，模拟设计变量的0/1约束，建立了用于最大化填充多孔弹性材料的夹层结构传声损失(TL)的浮动投影拓扑优化方法(FPTO)。给出了一些 2D 和 3D 数值例子来证明所提出的拓扑优化算法的能力和有效性。结果表明，多孔弹性材料的分布往往集中在一些位置。考虑到制造的容易性和对不确定外部载荷的抵抗力，传统的夹层结构通常具有周期性的芯材。所以，本文还研究了隔声周期性结构的拓扑优化。数值算例表明，优化的夹芯周期性芯材使多孔弹性材料在设计范围内均匀分布，但对隔声性能略有削弱。