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Wavelet Method for Calculating the Defect States of Two-Dimensional Phononic Crystals

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Abstract

Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants (mass density and elastic stiffness) in periodic wavelets, the explicit formulations of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. The point and line defect states in solid-liquid and solid-solid systems are calculated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China

    Zhizhong Yan & Yuesheng Wang

  2. Department of Civil Engineering, University of Siegen, D-57076, Siegen, Germany

    Chuanzeng Zhang

Authors
  1. Zhizhong Yan
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  2. Yuesheng Wang
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  3. Chuanzeng Zhang
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Corresponding author

Correspondence to Yuesheng Wang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10632020), the German Research Foundation (No.ZH 15/11-1) and jointly by the China Scholarship Council and the German Academic Exchange Service (No.D/08/01795).

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Yan, Z., Wang, Y. & Zhang, C. Wavelet Method for Calculating the Defect States of Two-Dimensional Phononic Crystals. Acta Mech. Solida Sin. 21, 104–109 (2008). https://doi.org/10.1007/s10338-008-0813-6

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  • DOI: https://doi.org/10.1007/s10338-008-0813-6

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