Three-Phase Microstructure Topology Optimization of Two-Dimensional Phononic Bandgap Materials Using Genetic Algorithms

The bandgap, an important characteristic of the periodic structure, is dispersion-related, which can be designed by tailoring the layout of materials within the periodic microstructures. A typical example of a periodic structure is phononic crystals (PnCs), which are traditionally fabricated from two-phase materials. Herein, we investigate the topologies of periodic three-phase PnCs. The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm, and three case studies are proposed to obtain the following: (1) the maximum relative bandgap width, (2) the maximum absolute bandgap width, and (3) the maximum bandgap at a specified frequency. More importantly, the three-phase material provides significant advantages compared to the typical two-phase materials, such as a low-frequency bandgap. This research is expected to contribute highly to vibration and noise isolation, elastic wave filters, and acoustic devices.