Thickness optimization of plate-type acoustic metamaterials for lightweight broadband sound insulation beyond the mass law

Lightweight sound insulation panels that exceed the mass law across a broad frequency range are desirable in many noise control applications in which weight and space are constrained. Plate-type acoustic metamaterials (PAMs) consist of a thin baseplate with periodically attached masses. PAMs can achieve high sound transmission loss (STL) through anti-resonances, but this is typically limited to narrow frequency ranges, and achieving broadband improvements requires meticulous design of the mass distribution within the unit cell. To address the challenging problem of designing mass distributions in PAM unit cells for broadband STL improvements, this work formulates and solves a thickness optimization problem using a coupled vibro-acoustic finite element analysis model. Two design strategies are investigated. Firstly, single-target-frequency optimization, which maximizes the STL relative to the mass law at a specified target frequency, resulting in PAM unit cells with strong, distinct anti-resonances. Secondly, multi-target-frequency optimization that achieves STL improvement exceeding predefined target improvements over the mass law across broad frequency ranges by strategically distributing multiple anti-resonances within the target frequency range. The single-target-frequency designs demonstrated STL enhancements of at least 24.6 dB relative to the mass law at their respective target frequencies. The multi-target-frequency designs accomplished broadband STL improvements of 3, 6, and 9 dB under normal incidence over 246-1000 Hz, 450-988 Hz, and 590-962 Hz, respectively, thereby achieving continuously high STL performance beyond the mass law across wide frequency ranges. This demonstrates the strong potential of thickness-optimized PAMs as thin and lightweight solutions for broadband sound insulation.