Maximizing acoustic band gap in phononic crystals via topology optimization

Designing phononic crystals (PnCs) to exhibit the widest attainable band gap, or to encompass a designated frequency range, is imperative for the realization of PnCs tailored to specific functionalities. However, achieving a wide band gap of acoustic waves centered around a specified frequency remains a significant challenge. The challenge arises from the fact that the optimization objective function may be enhanced by disconnected air regions. Nonetheless, these disconnected regions obstruct the circulation of air, rendering PnCs devoid of practical engineering utility. In this study, we propose a topology optimization methodology aimed at crafting air/solid PnCs that maximize the band gap of acoustic waves at a specified central frequency. To ensure adequate air permeability within the PnCs, the optimization model incorporates the virtual temperature technique in conjunction with the minimum length scale technique. The topology of the PnC unit cell is represented with a low number of design variables through the material-field series expansion, and the Kriging-based optimization algorithm is used to solve the complicated optimization problem. Diverse optimized configurations are presented, and experimental findings compellingly underscore the efficacy of the proposed optimization approach in the design of phononic band gap crystals geared towards acoustic waves at the specified central frequency.