Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique  

作　　者：史志杰 汪越胜 张传增 

机构地区：[1]Institute of Engineering Mechanics,Beijing Jiaotong University [2]Department of Civil Engineering,University of Siegen

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第9期1123-1144,共22页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.51178037 and10632020);the German Research Foundation(DFG)(Nos.ZH 15/11-1 and ZH 15/16-1);the International Bureau of the German Federal Ministry of Education and Research(BMBF)(No.CHN11/045);the National Basic Research Program of China(No.2010CB732104)

摘　　要：A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.A multiple monopole （or multipole） method based on the generalized mul- tipole technique （GMT） is proposed to calculate the band structures of scalar waves in two-dimensional phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure is obtained. Some numerical examples are presented to validate the proposed method.

关 键 词：phononic crystal generalized multipole technique multiple multipolemethod multiple monopole method band structure eigenvalue problem 

分 类 号：O175.9[理学—数学]