基于辛数学方法的一维声子晶体禁带计算  

Symplectic method for calculation of band gap of one-dimensional phononic crystals

作　　者：刘铁权[1] 邓子辰[1,2] 周加喜[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710129 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《振动与冲击》2010年第12期102-105,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(10972182;10772147;10632030);国家基础研究计划973基金(2006CB601202);教育部博士点基金(20070699028);西北工业大学基础研究基金;西北工业大学研究生创业种子基金(Z200930);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助项目

摘　　要：将一维声子晶体的原胞简化为有限多个自由度的弹簧振子结构,在辛对偶变量体系下探讨晶格振动,引入辛数学方法确定波矢与本证值的色散关系。通过本证值计数法计算特征频率,从而得到禁带区间。与传统集中质量法相比,该算法的计算结果与之吻合很好,且提高了计算精度和计算效率,更重要的是在低频处收敛性更好。The unit cell of one-dimensional phononic crystal was reduced to a spring-mass structure with limited number of degrees of freedom.The lattice vibrations were investigated in agreement with the dual variables system,and the dispersion relation was obtained by the symplectic mathematical method.Furthermore,the eigenfrequency was given by using the Wittrick-Williams algorithm,thus the band gap was obtained.Comparing the results calculated by the present method with those by the traditional lumped-mass method,it is obvious that there is a good agreement.However,the former is capable of improving the calculation accuracy and computational efficiency,and more importantly,is of better convergence.

关 键 词：声子晶体 禁带 辛方法 色散关系 集中质量法 

分 类 号：O302[理学—力学] O321