Shape optimization of studs in double-leaf plasterboard walls for maximal broadband sound insulation and minimal material use

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.