The cross-sectional shape of the metal studs in a double-leaf wall has a significant influence on its sound insulation. In a recent study, a numerical optimization of the stud shape resulted in designs that offer a significant increase in broadband airborne sound insulation, both when compared to conventional C-shaped studs and commercially available acoustic studs, but at the expense of a much higher material use. In the present work, a multi-objective optimization of the stud shape is aimed at, so as to find an optimized trade-off between the stud material cost and the sound insulation of the overall system across the entire building acoustics frequency range. This is achieved by combining a computationally efficient, iterative multi-objective optimization scheme with a computationally efficient numerical sound insulation prediction model of sufficient accuracy. Pareto fronts, which represent the set of optimal combinations of sound insulation and stud material use, are computed for a range of plasterboard wall systems that differ in cavity depth, number of sheets of plasterboard and stud type (symmetric or point-symmetric). For nearly all walls with symmetric studs, the Pareto fronts show that the introduction of a single deep indentation in the stud results in a high increase in sound insulation at a limited increase in material cost compared to simple C-shaped studs while two or three deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. For nearly all walls with point-symmetric studs, the Pareto fronts show that the introduction of two deep indentations results in a high increase in sound insulation at a limited increase in material cost compared to Z-shaped studs while four deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. It is shown that often, the acoustic performance of commercially available acoustic stud shapes can be further improved with less material used to produce the stud and sometimes even a shallower cavity.

双叶墙中金属立柱的横截面形状对其隔音效果有显着影响。在最近的一项研究中，与传统的 C 形螺柱和市售声学螺柱相比，螺柱形状的数值优化导致设计显着提高了宽带空气隔音效果，但以更高的材料为代价采用。在目前的工作中，旨在对螺柱形状进行多目标优化，以便在整个建筑声学频率范围内在螺柱材料成本与整个系统的隔音之间找到优化的权衡。这是通过结合计算效率高的，迭代多目标优化方案，具有足够准确的计算效率数值隔音预测模型。帕累托前沿代表隔音和螺柱材料使用的一组最佳组合，是针对腔深度、石膏板片数和螺柱类型（对称或点对称）不同的一系列石膏板墙系统计算得出的。对于几乎所有具有对称螺柱的墙壁，帕累托前沿表明，与简单的 C 形螺柱相比，在螺柱中引入一个深凹痕可大幅提高隔音效果，同时材料成本增加有限，而两个或三个深凹痕导致更高的材料成本，其性能接近具有解耦叶片的墙的性能。对于几乎所有带有点对称螺柱的墙，帕累托前沿表明，与 Z 形螺柱相比，引入两个深压痕可在材料成本增加有限的情况下大幅提高隔音效果，而四个深压痕导致更高的材料成本，其性能接近于墙与解耦的叶子。结果表明，通常可以使用更少的材料来生产螺柱，有时甚至是更浅的腔体，从而可以进一步提高市售声学螺柱形状的声学性能。