圆管型局域共振声子晶体三维构型振动带隙研究

Study on the 3D polarization band gaps of pipe-shaped locally resonant phononic crystals

采用多重多级子结构方法计算具有一定刚度的圆管型局域共振声子晶体三维构型振动带隙特性。考察包裹方向对带隙特性的影响,并对第一带隙上下边界点的单胞振动形式进行分析。结果表明,两种包裹形式都可以得到较低较宽的第一带隙,并且带隙特性相似,因而其周期结构都可以大幅减弱带隙范围内弹性波的传播。但两种构型带隙上下边界点对应振动形式不同,此外带隙特性还受单胞尺寸的影响。通过给定评价指标得到相关材料参数与带隙特性关系的相图,由此分析包裹层材料属性对带隙特性的影响。

The 3D polarization band gaps of pipe-shaped locally resonant phononic crystals with some certain stiffness are studied based on the multi-level substructure method.The influence of different wrapping directions on the 3D polarization band gaps is discussed.Moreover,the vibration modes under the frequencies of the maximum of the underlying bands and the minimum of the overlying bands of the first band gaps are discussed.The results show that relatively low and wide band gaps can be achieved by both of the two wrapping directions.The 3D polarization band gaps of the two kinds of cells are similar,so the periodic structures of these kinds of phononic crystals will help to prevent the propagation of some wide frequency range of elastic waves in relatively low frequency level to some extent.However,their vibration modes at the boundary of the band gaps are different.In addition,3D polarization band gaps will be influenced by the size of the cells.Moreover,the influence of the wrapping materials on the band gaps is discussed through the relationship between related materials and the band gaps evaluation concluded in a phase diagram.