A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals
A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals
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DOI：
10.3970/cmes.2008.038.059
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发表时间：
2008-12
影响因子：
2.4
通讯作者：
Zhi-Zhong Yan;Yuesheng Wang;Chuanzeng Zhang
中科院分区：
文献类型：
--
作者：
Zhi-Zhong Yan;Yuesheng Wang;Chuanzeng Zhang
本文提出了一种基于小波理论的数值方法，用于计算由一般各向异性材料组成的二维声子晶体的能带结构。在对小波的选择进行了系统的考虑后，选择了Haar小波和双正交小波两种小波。结合超原胞技术，该方法可用于计算点缺陷和线缺陷声子晶体的能带结构。我们说明了数学和数值方法的优点。特别是对具有复杂晶格结构的各种材料组合（固-固、固-流和流-流）给出了一些有代表性的数值算例，以显示该方法的精度、快速收敛性和广泛的适用性。
In this paper, a numerical method based on the wavelet theory is developed for calculating band structures of 2D phononic crystals consisting of general anisotropic materials. After systematical consideration of the appropriate choice of wavelets, two types of wavelets, the Haar wavelet and Biorthogonal wavelet, are selected. Combined with the supercell technique, the developed method can be then applied to compute the band structures of phononic crystals with point or line defects. We illustrate the advantages of the method both mathematically and numerically. Particularly some representative numerical examples are presented for various material combinations (solid-solid, solid-fluid and fluid-fluid) with complex lattice structures to show the accuracy, fast convergence and wide applicability of the method.