二维声子晶体微腔能带结构的有限元分析与设计

Finite Element Analysis and Design of Band Structures for Two-dimensional Phononic Crystals Microcavity

本文基于ABAQUS建立了二维声子晶体体波能带结构的有限元计算方法。该方法首先利用周期性边界条件和Bloch定理,将周期结构的有限元离散特征方程化归到一个周期单胞内的复系数特征方程,然后将其分为实部和虚部两组方程,并在周期单胞边界上应用Bloch定理,求解得到的实数特征方程,获得频散曲线。与已有计算方法相比,该方法在适用性、计算速度、精确度和收敛性等方面具有明显的优越性。在此基础上使用发展的有限元方法分析研究了不同形状的声子晶体微腔的能带结构特性。结果表明这些晶体结构对于特定频率的声波可以将其限制在声子晶体微腔内,在一定环境下有着较好的吸声降噪功能。

This paper presents a calculation method based on the ABAQUS for band structures two-dimensional （2D） phononic crystals.An eigenvalue equation with complex coefficients for a unit cell is derived from the eigenvalue equation of the discretization form for the whole periodic structure by considering the periodic boundary conditions and Bloch theory.Then,the above equation is divided into two sets with real coefficients.And the Bloch conditions are imposed on the edge nodes of the unit cell.Therefore,the obtained eigenvalue problem can be solved to yield the dispersion relations.It is shown that the developed method has advantages over other methods in flexibility,calculation speed,accuracy and convergence.The band structures of 2D phononic crystals with microcavities of different shapes are analyzed by using the developed method.The results show that elastic waves with particular frequencies can be confined in the phononic crystal resonant cavity.These structures have a better sound absorption and acoustic noise reduction in certain circumstances.