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A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals

Zhi-Zhong Yan1,2, Yue-Sheng Wang1,3, Chuanzeng Zhang2
Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China
Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany
Corresponding author. Tel: +86-10-51688417, E-mail:yswang@bjtu.edu.cn

Computer Modeling in Engineering & Sciences 2008, 38(1), 59-88. https://doi.org/10.3970/cmes.2008.038.059

Abstract

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.

Keywords

elastic wave, phononic crystal, band structure, wavelet, numerical method

Cite This Article

Yan, Z., Wang, Y., Zhang, C. (2008). A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals. CMES-Computer Modeling in Engineering & Sciences, 38(1), 59–88.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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