基于边界元法的非完好界面三角晶格声子晶体带隙计算

Band-gap Calculations of Phononic Crystals in a Triangular Lattice with Imperfect Interfaces Based on the Boundary Element Method

采用边界元法研究了具有非完好界面条件的二维三角晶格声子晶体的带隙特性。结合Bloch周期原理,针对二组元三角晶格固-固体系声子晶体推导了含非完好界面条件的边界元特征值方程。基于该方程,计算了含有不同截面散射体(圆形截面、椭圆截面、正方截面)的能带结构,讨论了晶格对称性对能带结构的影响;并且分析了圆形截面散射体填充比的变化对带隙位置及宽度的影响。通过与其它计算方法的结果比较,说明边界元法可以有效准确地计算具有不同界面条件和不同散射体形状的声子晶体的能带结构。而且,非完好界面条件的声子晶体可以在低频打开完全带隙,尤其圆形截面最为明显。

The bandgap characteristics of two-dimensional phononic crystals in a triangular lattice with imperfect interface conditions were studied by using the boundary element method. Combined with Bloch theorem,the boundary element eigenvalue equations with imperfect interface conditions were derived for the two-component solid-solid phononic crystal in a triangular lattice. Based on the equation,the band structures of phononic crystals with different cross-section scatterers( circular,elliptical and square cross-section) were calculated,and the effects of the lattice symmetry on the band structures were discussed;additionally,the influences of the scatterer filling ratio on the position and width of the bandgaps were analyzed in the case of circular cross-section. Compared with other results calculated by other methods,it is shown that the boundary element method can effectively and accurately calculate the band structures of phononic crystals with different interface conditions and different shaped scatterers. Moreover,phononic crystals with imperfect interface conditions can open the complete band gap at low frequencies,especially for the phononic crystals with the circular cross-section.