Topological design of phononic crystals for multiple wide band gaps

Most existing phononic crystals (PnCs) are characterized by a single band gap, and for crystal systems that require multiple band gaps, the method of assembling multiple configurations with different gaps can seriously complicate the manufacture procedure, which hinders their potential applications. In this work, a multiple band gap topological optimization strategy is proposed to design a two-dimensional PnC with the objective of maximizing the specified number of relative band gaps in the in-plane or out-of-plane modes. The topology optimization problem is formulated based on the material-field series-expansion model and solved using a gradient-free algorithm. Calculations of the transmission curves and amplitude fields at typical frequencies confirm the validity of the optimized designs. In addition, PnC unit cells with multiband gaps are used to obtain PnC resonators, and their energy band structure and localization effects are investigated. It is found that these PnC resonators introduce many flat defect bands within each complete forbidden band, which give rises to multifrequency localization effects and promotes their facilitation in energy harvesting technologies.