Narrow-band filter design of phononic crystals with periodic point defects via topology optimization

Abstract Designing multichannel narrow passband filters working at specified frequencies is very challenging because a narrow defect band with non-zero group velocity must be achieved. This study proposes an effective topology optimization methodology for designing periodic defect unit cells in the bandgap supercell to form a specified narrow passband within the desired frequency range. A new topological optimization formulation aiming to determine the highest transmission rate around specified frequency of supercells is developed. The complicated topology configurations of the perfect bandgap unit cell and periodic defect unit cell are both described by only fifty design variables with the material-field series expansion model, and the optimization problem is solved with the sequential Kriging-based non-gradient algorithm. Through the proposed methodology, several narrow passband filtering supercell configurations with different specified frequencies are achieved. Furthermore, a multi-channel narrow filter conceptual device that can split the incident waves of three similar frequencies is designed with the optimization solutions.