Band structure calculations of in-plane waves in two-dimensional phononic crystals based on generalized multipole technique

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• 作者：Zhijie Shi ; Yuesheng Wang ; Chuanzeng Zhang
• 关键词：phononic crystal ; generalized multipole technique (GMT) ; multiple monopole (MMoP) method ; band structure ; eigenvalue problem ; fluid ; solid interaction condition ; O175.9 ; O735 ; 15A18 ; 78M16
• 刊名：Applied Mathematics and Mechanics
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：36
• 期：5
• 页码：557-580
• 全文大小：5,916 KB
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• 作者单位：Zhijie Shi (1)
  Yuesheng Wang (1)
  Chuanzeng Zhang (2)
  
  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China
  2. Department of Civil Engineering, University of Siegen, Siegen, D-57068, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics
  Mathematical Modeling and IndustrialMathematics
  Chinese Library of Science
  
• 出版者：Shanghai University, in co-publication with Springer
• ISSN：1573-2754

文摘

A numerical method, the so-called multiple monopole (MMoP) method, based on the generalized multipole technique (GMT) is proposed to calculate the band structures of in-plane waves in two-dimensional phononic crystals, which are composed of arbitrarily shaped cylinders embedded in a solid host medium. To find the eigenvalues (eigenfrequencies) of the problem, besides the sources used to expand the wave fields, an extra monopole source is introduced which acts as the external excitation. By varying the excitation frequency, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and the boundary of the irreducible first Brillouin zone (FBZ), the band structures can be obtained. Some typical numerical examples with different acoustic impedance ratios and with inclusions of various shapes are presented to validate the proposed method.