Comprehensive analysis of band gap modulation of hexagonal fan blade and optimized ligament structure in the low-frequency range

Abstract

This paper proposed a meta material model with low-frequency wide band gap and band gap tunability, optimized its structure as a multibranch chain structure, and analyzed the band gap relationship of above two models based on Brag's theorem and finite element method. Among them, the fan base structure has a band gap of 65.92 % within 20,000 Hz, and the band gap is optimized to low-frequency after the structure is optimized, and the band gap reaches 75.94 % within 10,000 Hz. The effects of the ligament width and the thickness of the center parcel layer on the band gap distribution of the structure are also discussed, and the wave transmission characteristics in the structure are explored by group and phase velocities to verify the acoustic performance of the structure. The results show that the smaller the ligament thickness is, the lower the first band gap opening frequency of the structure is; when the thickness of the central wrapping layer is increased, the structure develops the band gap at the center frequency of 3000 Hz to a lower frequency and generates an ultra-wide band gap at the center frequency of 6000 Hz. These findings can provide a new idea for low-frequency vibration isolation and noise reduction.