Multi-objective topology optimization of two-dimensional multi-phase microstructure phononic crystals

The band gap (BGs) of a material can be manipulated by tailoring its periodic microstructure. The phononic crystals (PnCs), representative of a periodically arranged structural material, are conventionally manufactured from single-phase or two-phase materials. In this study, we investigate the multi-objective topology optimization (MOTO) of periodic three-solid-phase PnCs. With a method of two-stage multi-objective genetic algorithm, the microstructures of the three-solid-phase PnCs were designed to exhibit the desired novel properties. Three case studies were obtained as follows: (1) maximum relative band gap width (RBGW) with a minimum mass, (2) maximum absolute band gap width (ABGW) at two different specified frequencies, and (3) maximum ABGW at specified mid-frequency. All the cases were effective for the MOTO of PnCs, and the Pareto optimal solution set could give the balance of the different competed objectives. Further, the principal mechanisms responsible for the creation of BGs, whether Bragg scattering or local resonance, are discussed. Moreover, comparing with the normal 2-phase materials, suchlike a wider lower-frequency BGs, some important advantages unveiled with the appearance of the three-solid-phase material.