Optimization of graded and partial metamaterial treatments for enhanced broadband sound insulation in partition panels

Resonant metamaterials can achieve unprecedented vibroacoustic attenuation in lightweight partition panels through small resonators attached on a subwavelength scale. Conventional metamaterial treatments are effective only in a narrow band and typically cover the entire panel surface, posing important challenges for industrialization due to manufacturing and cost constraints. To address these issues, in this study we propose graded and partial metamaterial treatments, which are selectively distributed where they are the most effective, avoiding unnecessary coverage, and include a spatially varying resonance frequency for broadband effectiveness. The related design challenges are tackled by developing a numerical methodology that simultaneously optimizes the distribution and the grading of the treatment. The optimization objective is to maximize the broadband diffuse sound transmission loss (STL) of the metamaterial panel, while constraining the maximum fraction of treated area. Leveraging effective medium modelling, the approach efficiently incorporates local changes in the effective mass density of the metamaterial panel to represent partial treatments. Different design cases are considered for different target bands and panel dimensions. Results demonstrate that graded partial metamaterial treatments can achieve broadband improvements with a limited treated area, effectively suppressing the STL dips due to the modes of the host panel and to coincidence effects.