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Acta Mechanica Solida Sinica

, Volume 21, Issue 2, pp 104–109 | Cite as

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

  • Zhizhong Yan
  • Yuesheng Wang
  • Chuanzeng Zhang
Article

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.

Key words

acoustic wave phononic crystal defect state wavelet band structure 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2008

Authors and Affiliations

  1. 1.Institute of Engineering MechanicsBeijing Jiaotong UniversityBeijingChina
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany

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