用传递函数法研究三谐振局域共振的能带结构

A study on energy band structure of three resonant local resonance by transfer function method

利用传递函数研究局域共振声学超材料能带结构的形成,得到一维局域共振周期结构的递归方法.用传递函数的表达式确定有限超材料中带隙形成的机制.将有限声学超材料动力学分析与无限长超材料布洛赫定理分析进行比较,表明了用传递函数法计算带隙的正确性,得出系统极点作用产生了带隙和通过传递函数法改变原胞数目来调控带隙范围的结论.

In this paper,the local resonance acoustic metamaterial band structure has been studied with the transfer function,and the recursive method of one-dimensional local resonance periodic structure has been obtained.The mechanism of the band gap formation in a finite metamaterial is determined by the expression of the transfer function.Comparing the finite acoustic metamaterial dynamics analysis with the infinite-length metamaterial Bloch theorem,it is shown that the correctness of the bandgap can be calculated by the transfer function method,and the band-effect of the system pole can be generated and changed by the transfer function method when it comes to the number of primitive cells to control the band gap range.