The Phononic Properties and Optimization of 2D Multi-Ligament Honeycombs.

Honeycomb structures have attracted much attention for their excellent characteristics of reducing vibration and noise in recent years. In this study, through band analysis of different ligament structures, we aim to optimize the design of a steel structure that can isolate most of the noise in the 1500-5000 Hz range. The present study examines several different chiral structures. We calculate the band gaps of chiral structures under different geometric configurations and identify the variations in band gaps with geometric layouts. It is found that compared to other chiral structures, the triligaments chiral structure exhibits excellent band gap characteristics. The calculation results demonstrate that enhancing axial symmetry while filling central nodes can effectively enhance the structure's band gap properties. Frequency-response functions of different lattice structures are computed, and the results align with the calculations of band structures. This study then analyzes the influence of the number of periods on the magnitude of vibration attenuation, revealing that under the same number of periods, the wider the band gap of the structure, the greater the vibration attenuation. Both the triligaments chiral structure and the vertical triligaments structure possess ideal band gap widths, effectively suppressing wave propagation. Subsequently, harmonic response analyses and transient wave calculations further validate the accuracy of the band structure and frequency-response curve calculations. Our study results provide a new way to design a sound insulation structure that can isolate noise signals within the frequency range from 1500 to 5000 Hz in engineering.