三相声子晶体能带结构计算的位移-面力映射方法

The method based on displacement-traction map for calculation of the dispersion relation of three-phase phononic crystals

发展了基于位移-面力映射的方法计算三相声子晶体的能带结构,分析了弹性波在其中传播的特性。由弹性动力学方程出发,利用位移-面力映射,导出波动模态的特征值方程,得到三相局域共振声子晶体反平面剪切波的频散关系(即能带结构)。以金-橡胶-环氧树脂体系为例,计算并分析了材料组配、几何尺寸等对频散关系造成的影响。研究结果显示:位移-面力映射方法非常有效,可以给出任意频率范围内弹性波的局域模态和传播模态,为分析三相体系局域共振形成的低频带隙和布拉格散射形成的带隙提供了方便。

This paper develops the method based on displacement-traction map to compute the dispersion curve of three-phase phononic crystals,and analyses the propagating feature of elastic waves in it. Beginning with the elastic dynamic equation ,we use column wave function expansion attribute scattering wave field to set up displacement-traction map, then we can derive the vibration mode eigenvalue equation fi＇om Bloch theorem, at last the dispersion relations （i.e.Band structure）of three-phase resonant phononic crystals is obtained. Taking the system of Aurum- Epoxy-Rubber as an example ,this paper calculates and analyses the influence of materials group and geometric size. The results of the study show that the method based on displacement-traction map is so effective that can give resonant model and propagating model of the elastic waves in any frequency range. This will do good to analysis of low frequency band-gap due to resonant vibration and the band-gap due to Bragg scattering.