基于声子晶体带隙特性的薄板减振设计

Vibration Reduction Design of Thin Plate Based on Band Gap Features of Phononic Crystals

基于平面波展开法和薄板振动方程,计算了薄板型声子晶体的带隙和减振特性,通过与有限元软件的计算结果验证带隙计算的正确性,并进一步讨论了散射体几何形状及填充率、弹性模量比、密度比等对薄板型声子晶体带隙特性和减振的影响。结果表明正多边形散射体随边数的减小,第一带隙宽度逐渐增加,正方形散射体薄板减振效果明显。填充率对声子晶体带隙特性的影响不是线性的。随散射体基体弹性模量比数量级增大,第一带隙趋于低频,宽度降低。散射体基体弹性模量比较大时,密度比越大,第一带隙宽度越大,对应的薄板结构减振特性越好。

Based on the plane wave expansion method and the wave equations,the band gap and the vibration reduction features of the thin plate can be calculated. The comparison of the results between commercial software and the developed program can validate the established model. The effects of the geometry of the scatters,the filling factor,the ratio of the elastic modulus and the density ratio on the band gap and the vibration reduction are further studied. Results indicate that the first band gap can be decreased with the increase of the side number of the polygonal scatters. Square scatter shows better vibration reduction. The effect of the filling factor on the band gap of the phononic crystal is not linear.With the increase of the ratio of the elastic modulus in order of magnitude,the frequencies and the width of the first band gap can be decreased. When the ratio of the elastic modulus is high,the width of the first band gap can be increased with the increase of the density ratio. The vibration of the corresponding thin plate can be reduced.