基于1维石灰岩／硅橡胶声子晶体的振动控制研究

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In this paper, the lumped mass method is employed to computerize the band gap property of the one-dimensional phonon crystal of limestone and silicone rubber. The regulation of the structural and material parameters on the band gap is analysed systematically. Studies show that, the frequency of the band gap moves towards the low region and the width of the band gap is narrowed as the lattice constant of the structure is increased; when increase the density difference of the two materials or the elastic modulus of the difference of the two materials, low-frequency and broadband band gap can be obtained; when regulate the thickness of the silicone rubber or the component ratio, low-frequency, broadband band gap can be obtained as well; when t=0. 426, the first and second band gap and ending frequency drop to medium-low frequency, within 1 kHz, the impact of the Poisson＇s ratio of the material changes in the band gap can be ignored. Overall, one-dimensional element limestone and silicone rubber rod phonon crystal has the characteristics of forbidden band in medium-low frequency. Vibration control requirements can be achieved by adjusting the relevant parameters, which is of theoretical significance as to using the vibration control devices of elastic wave or acoustic wave filters in the low frequency band.采用集中质量法计算了1维石灰岩/硅橡胶杆状声子晶体的带隙情况,系统分析了该声子晶体模型的结构参数和材料参数对带隙的调控规律.研究表明：结构的晶格常数增大时,带隙频率趋向低频率区域,带隙宽度变窄;增大两种材料的密度差值,或者增大两种材料的弹性模量差值,能够获得低频、宽带带隙;调节硅橡胶的厚度或组份比t也可以获得低频、宽带带隙,当t=0.426时,第1,第2带隙的起止频率下降到中、低频率1kHz以内;材料的泊松比变化对带隙影响可以忽略.总体而言,1维2组元石灰岩/硅橡胶杆状声子晶体具有中、低频率段的禁带特征,通过调节其相关参数可以实现不同的振动控制要求,对利用该声子晶体制备中、低频率段的弹性波/声波滤波振动控制器件具有一定的理论意义