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

作　　者：Zhijie SHI Yuesheng WANG Chuanzeng ZHANG 

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)》2015年第5期557-580,共24页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10632020);the German Research Foundation(Nos.ZH 15/11-1 and ZH 15/16-1);the International Bureau of the German Federal Ministry of Education and Research(No.CHN 11/045);the National Basic Research Program of China(No.2010CB732104)

摘　　要：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.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.

关 键 词：triangular validate impedance excitation collocation searching elliptical cylinders irreducible scattered 

分 类 号：O735[理学—晶体学]