Optimum design of a multi-functional acoustic metasurface using topology optimization based on Zwicker's loudness model

In this paper, we construct the optimum design method for the multifunctional acoustic metasurface that is permeable and provides soundproofing characteristics by topology optimization method. The permeability of the metasurface is due to the network of through holes. The soundproofing aspects of the acoustic metasurface are obtained using a topology optimization based on Zwicker's loudness model, which aims to represent the characteristics of the human auditory system, and we use Zwicker's loudness model to evaluate perceived loudness levels. We represent the acoustic-elastic coupled system using a two-phase material model in which the solid and acoustic phases are mixed. We adopt a level set-based topology optimization method and observe how the metasurface configuration obtained by the proposed method operates to provide soundproofing, finding that transmission waves in a wide band are reduced due to multi-phenomena, namely Wood's anomaly and resonances in the two types of cavity present in the metasurface. Moreover, we also optimize sound blocking in a system that is unresponsive to transverse waves and compare the results with those of an optimum structure obtained by optimization of an acoustic-elastic coupled system. Finally, we demonstrate the utility of the proposed method and conclude that it facilitates the design of efficient multi-functional metasurfaces that can reduce humanly perceived loudness in a wide band.