Broadband acoustic shape optimization of studs in double-leaf walls

Design optimization of vibro-acoustic systems over a wide frequency band is challenging. It does not only require a computationally efficient numerical prediction model of sufficient accuracy, but the optimization scheme itself should also be computationally efficient and the design space should be limited by all relevant manufacturing and performance constraints. In this paper, a methodology is presented for the shape optimization of components in a complex wall system, with the aim of achieving an optimized sound insulation of the overall system across the entire building acoustics frequency range. As an example, the cross-sectional shape of studs in a double-leaf wall is first parameterized and subsequently optimized for broadband sound insulation with a gradient-based optimization scheme. A recently developed sound insulation prediction model that has the required balance between accuracy and computational efficiency is adopted and validated for a range of plasterboard walls with acoustic studs. The model is further complemented with a novel sensitivity analysis, such that the sensitivities of the predicted sound insulation to the cross-sectional stud shape parameters can be obtained in a semi-analytic way. This approach reduces the computation cost related to broadband acoustic design optimization significantly. Furthermore, inequality constraints that are necessary for obtaining a feasible design in terms of material usage and manufacturing limitations are identified and incorporated in the optimization procedure. The relevant constraints related to strength and stiffness of the wall are very mild and therefore verified after optimization. As an example of the proposed methodology, the cross-sectional shape of flexible metal studs in double-leaf plasterboard walls is optimized for the overall A-weighted sound reduction under pink noise excitation. A range of combinations in stud depths and number of sheets is analyzed. Walls containing the optimized studs have an airborne sound insulation that is close to that of walls with fully decoupled leafs. Their sound insulation is on average 11.8 dB higher than when they would contain conventional C-shaped studs, and 5.1 dB higher than when they would contain acoustic studs that are presently available.