Sizing optimization of multiple Helmholtz resonators for low-frequency broadband sound absorption

Noise control is a critical issue in modern environments such as vehicles, buildings, and industrial sites. Conventional sound-absorbing materials such as polyurethane foam and glass wool have been widely used to address these challenges. However, these materials exhibit poor performance in the low-frequency range, and achieving sufficient absorption at low frequencies typically requires bulky components. To meet demands for compact and efficient noise control, especially in low-frequency ranges, advanced sound-absorbing structures are needed. This study proposes a design method for sound-absorbing structures that achieve high absorption coefficients over a broad low-frequency range by optimizing the dimensions of multiple Helmholtz resonators. First, the absorption characteristics of the resonators are evaluated using the transfer matrix method. Next, a sizing optimization problem is formulated to maximize the absorption coefficient within a target frequency band, using the resonator dimensions as design variables. Numerical examples are presented where the optimization problems are solved using a gradient-based method. Results are shown for two cases: one where only the neck dimensions are used as design variables, and another where both neck and cavity dimensions are considered. Finally, the validity of the proposed designs is confirmed through the finite element method (FEM) analysis.