功能梯度声子晶体中纵波带隙分析

Study of Band Gap of Longitudinal Wave in Functionally Graded Phononic Crystal

基于功能梯度指数形式变化的杆件中纵波的解析解,构造了一种周期内由两层梯度材料构成的声子晶体(周期结构),并利用传递矩阵方法计算和绘制了该结构中纵波的频散曲线。该模型克服了传统功能功能梯度材料的波动问题中控制方程是变系数偏微分方程组难以求解的困难。分析和探讨了各种材料变化参数对该周期结构带隙宽度的影响。通过研究发现,声子晶体的带隙有奇数阶和偶数阶之分,并且由不同的材料变化参数所控制。

Based on analytical solution of longitudinal wave in functionally graded bar with exponential var-iable, a kind of phnonic crystal （periodic structure） which has two graded layers in one period was con-structed. Dispersion curves was computed and plotted by transverse matrix method. In virtue of this mo-del, difficulty of solving the partial differential equations was conquered on wave in traditional functionally graded material. The influences of variable parameters of material property on width of band gap of pho- nonic crystal were investigated. It can be concluded that band gap may be divided into even-order and odd-order and may be dominated by different variable parameters of material property.