偶应力一维声子晶体中出平面Bloch波的色散特征  

Dispersion Feature of Anti-plane Bloch Waves in 1-D Phononic Crystal with Couple-stress Elasticity

作　　者：李月秋[1] LI Yue-qiu(Faculty of Science,Qiqihar University,Qiqihar 161006,China)

机构地区：[1]齐齐哈尔大学理学院数学系

出　　处：《数学的实践与认识》2018年第21期134-140,共7页Mathematics in Practice and Theory

基　　金：黑龙江省省属高等学校基本科研业务费科研项目(135109232)

摘　　要：研究了由偶应力固体构成的周期层状结构中出平面Bloch波的色散关系.首先,给出偶应力固体中自由能密度表达式,得到了本构关系,并进一步得出位移形式的运动方程;然后,根据偶应力固体的界面条件,计算出一个典型单胞的状态矢量;再根据传递矩阵和Bloch定理,推导出Bloch波的色散关系,最后,根据数值结果讨论了微结构参数对出平面Bloch波的色散曲线以及带隙的影响.The dispersive relations of Bloch waves in the periodically laminated structure formed by periodically repeating of two different couple-stress elastic solids are studied in this paper. First, the motion equation and interface conditions are formulated in the couplestress elastic solid Apart from the bulk waves, there are evanescent waves which become shear type surface waves at the interface of two different couple-stress elastic solids. The continuous conditions of the interface are used to derive the transfer matrix of state vector in a typical single cell. At last, the Bloch theorem is used to give the dispersive equation of Bloch waves in the periodical structure. The numerical results are obtained by solving the dispersive equations and shown graphically. The influences of the microstructure parameter of the couple-stress elastic solid on the dispersive relations of anti-plane Bloch wave are discussed based on the numerical results.

关 键 词：偶应力弹性 声子晶体 Bloch波 色散关系 带隙 

分 类 号：O735[理学—晶体学]