Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique
Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique
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DOI：
10.1007/s10483-013-1732-6
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发表时间：
2013-07
影响因子：
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通讯作者：
Zhi-jie Shi;Yuesheng Wang;Chuanzeng Zhang
中科院分区：
文献类型：
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作者：
Zhi-jie Shi;Yuesheng Wang;Chuanzeng Zhang
提出了一种基于广义多极技术（GMT）的多单极（或多极）方法来计算二维声子晶体中标量波的能带结构，该二维声子晶体由嵌入主介质中的任意形状的圆柱体组成。为了找到问题的特征值，除了用于扩展波场的源外，还引入了一个额外的单极子源作为外部激励。通过改变激励频率，可以将特征值定位为适当选择的函数的极值点。通过扫描感兴趣的频率范围并扫描不可约第一布里渊区的边界，获得能带结构。给出了一些数值例子来验证所提出的方法。
A multiple monopole (or multipole) method based on the generalized multipole technique (GMT) is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.