Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals
Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals
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基于小波的二维声子晶体弹性带隙计算方法
DOI：
10.1103/physrevb.74.224303
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发表时间：
2006-12
影响因子：
3.7
通讯作者：
Wang, Yue-Sheng
中科院分区：
文献类型：
--
作者：
Yan, Zhi-Zhong;Wang, Yue-Sheng
提出了一种计算二维声子晶体弹性带隙的小波方法。波场展开的小波基和一个等价的特征值问题推导出一个矩阵形式的自适应计算的小波积分。该方法适用于一个二进制系统。我们首先计算环氧树脂基质中Au圆柱的带隙。与著名的平面波展开法的优点，基于小波的方法进行了讨论。然后用该方法计算了弹性常数比Au小${10}^{6}$倍的软橡胶中Au柱的带隙。收敛性检验表明，小波变换方法在一定程度上可以消除吉布斯效应。这些优点使得传统平面波方法难以解决的固-流混合声子晶体能带结构的计算变得容易。此外，小波的自适应性使得该方法可以有效地计算更复杂的声子结构的带隙。
A wavelet-based method is developed to calculate elastic band gaps of two-dimensional phononic crystals. The wave field is expanded in the wavelet basis and an equivalent eigenvalue problem is derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method is applied to a binary system. We first compute the band gaps of Au cylinders in an epoxy host. The advantages of the wavelet-based method are discussed in regard with the well-known plane-wave expansion method. Then the method is used to compute the band gaps of Au cylinders in a soft rubber with elastic constant ${10}^{6}$ times lower than that of Au. The convergence tests show that the wavelet-based method can reduce the Gibbs effect to a certain extent. These advantages make it possible for easy calculations of band structures of mixed solid-fluid phononic crystals where the traditional plane wave method encounters difficulties. In addition, the adaptability of wavelets makes the method possible for efficient band gap computations of more complex phononic structures.