Energy-based topology optimization for designing acoustic metasurfaces with permeable openings

In previous studies, designing acoustic metasurfaces with openings using topology optimization required predefining the opening areas without material, as improving insulation tended to close the design domain. In this study, we propose two novel methods for designing acoustic metasurfaces with openings using topology optimization without explicitly setting the opening area. The first method minimizes acoustic energy at the target frequency within a specified region while maximizing low-frequency energy to ensure permeability. The second method maximizes the reactive intensity component around the design domain, resulting in shapes resembling multiple resonators. We employ a level-set-based topology optimization approach using the reactive diffusion equation and introduce topological derivatives as sensitivity information. Optimization is performed under incident waves with multiple angles and frequencies. The acoustic phenomena generated by the optimized structures and their relationship to the objective functions are analyzed.