复合柱局域共振声子晶体的超宽带隙与可调性研究

Study on Characteristics and Tunability of Ultra-wide Band Gaps for Composite Column Locally Resonant Phononic Crystals

局域共振声子晶体因具有良好的低频带隙特性,在低频减振降噪方面具有广泛的应用前景。以设计一种具有超宽带隙的三组元二维复合柱声子晶体结构为目标,该结构由散射体、双包覆层和六棱柱基体板组成,相对应的局域共振单元附加质量比为65.13,利用有限元方法计算该声子晶体板的能带结构、传输损失谱和位移矢量场。结果表明:在0~3000 Hz的频率范围内相对带宽高达162.10%。与方形柱基体板声子晶体相比,所设计的六棱柱基体板声子晶体的第一完全带隙频率更低且第二带隙频率范围更宽。通过优化几何结构、改变材料参数以及引入压电效应等方式,实现对多条完全带隙的调控,并进一步拓宽完全带隙形成超宽带隙。研究结果可为研发可调低频减振降噪产品提供一定的理论参考。

Locally resonant phononic crystals,due to their unique band gap characteristics,have a wide application prospect in vibration and noise reduction in low-frequency ranges.In this paper,a two-dimensional three-component composite column phononic crystal is proposed.This crystal consists of a scatter,a double cladding layer and a hexagonal prismatic substrate plate with locally resonant unit additive mass ratio of 65.13.The band gap structures,transmission loss spectrum and displacement vector fields of the phononic crystal plate are calculated using the finite element method.The results show that the relative bandwidth of the crystal plate is up to 162.1%in the frequency range of 0-3000 Hz.The designed hexagonal prismatic matrix plate phononic crystal has a lower first complete bandgap frequency and a wider second bandgap frequency range than the square column matrix plate phononic crystal.By optimizing the geometrical structure,changing material parameters and introducing piezoelectric effects,the band gap width of this composite column phononic crystal can be tuned from 1382.00 to 2978.55 Hz flexibly.The results of this study may provide a theoretical reference for the prevention and control of low-frequency vibration and noise.