A bandgap optimization scheme for phononic crystals coupled with acoustic black hole structure

A new phononic crystal with an acoustic black hole (ABH) structure and a response surface methodology (RSM)-based optimization scheme for low-frequency bandgap design are proposed in this study. The band structure, formation mechanism, and attenuation characteristics of the proposed design were systematically investigated and compared with two reference models. Through single-factor analysis, six geometric parameters were screened, among which the ABH width, short edge height, and short board width were identified as the most influential on the first bandgap. A Box-Behnken design with 13 numerical experiments was then conducted using the finite element method, and second-order regression models were established to quantitatively link the three key parameters to the bandgap boundaries. The results show that the new phononic crystal exhibits a first bandgap of 12–805 Hz with 70% coverage below 40 Hz. The optimization framework enables accurate customization toward a target frequency range (10–600 Hz), with a maximum prediction error of only 2.0%, confirming its effectiveness as a predictive design tool for low-frequency vibration control.