Mechanism of low-frequency band gap formation in butterfly-shaped phononic crystals

To address the challenge of achieving low-frequency band gaps in Bragg phononic crystals, this paper proposes a novel butterfly-shaped phononic crystal composed solely of PLA. This structure enables independent tuning of the upper and lower edges of the complete band gap. Through finite element analysis of the band structure and eigenmodes, we identify the distinct mechanistic origins of each band edge: the upper edge is governed by wings vibrations, while the lower edge is controlled by central blocks vibrations. This decoupling allows for targeted manipulation via specific geometric parameters. Results demonstrate a complete band gap from 1273.8 Hz to 1477.5 Hz (bandwidth of 203.7 Hz). Crucially, we show that increasing the blocks length or blocks thickness selectively lowers the lower edge, while increasing the wings-end length selectively lowers the upper edge, thereby achieving independent control. The finite element method is used to calculate the transmission loss and transient transmission to verify the validity of the band gap range under the finite period, and experimentally verified. The results show that the phononic crystal structure has low-frequency band gap characteristics and can realize independent regulation of the upper and lower edges of the band gap, which is potentially applicable in the field of low-frequency vibration and noise reduction in charging piles.