二维内质量结构三角形晶格声子晶体的带隙研究

Study on the band gaps of two dimensional mass-in-mass structure triangular lattice phononic crystals

用集中参数模型理论研究具有内质量周期结构的二维三角形晶格声子晶体的带隙特性,设计了二维无限延伸的周期复合三角形晶格结构,通过理论及数值仿真发现改变质量和刚度可以人为调控带隙,最后与蜂窝状晶格的带隙进行对比.结果表明:晶体的色散曲线在频域上不连续,具有完全带隙的现象.晶体外部质量对带隙的影响最大,减小外部质量可得到较宽的带隙.此类结构中三角形晶格的带隙比六角蜂窝晶格的带隙少,但其带隙的宽度较宽,它为进一步带隙调控奠定良好的基础.

The band gap characteristics of two-dimensional triangular lattice phononic crystal of mass-in-mass periodic structure were studied based on the lumped parameter model. A two dimensional infinite complex triangular lattice system has been designed, and the fact that band gap can be artificially controlled by changing mass and stiffness has been proved by theory and numerical simulation. Finally, we have compared the band gaps of triangular lattice with honeycomb lattices. The results show that the dispersion curve of the crystal is not continuation in the frequency domain and have a full band gap. The external mass of crystal has the greatest influence on the band gap, and reducing the external mass can obtain the wide band gap. The band gap of triangular lattice is less than hexagonal honeycomb lattice, but its band gap width is wider. This lays a good foundation for further control of band gap.