立方准晶压电材料的半空间问题  

The Half Space Problem of Cubic Quasicrystal Piezoelectric Materials

作　　者：李光芳 刘昉昉 于静 李联和 LI Guangfang;LIU Fangfang;YU Jing;LI Lianhe(College of Science,Inner Mongolia Agricultural University,Hohhot 010018,P.R.China;Center for Applied Mathematics Inner Mongolia,Hohhot 010022,P.R.China;College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,P.R.China)

机构地区：[1]内蒙古农业大学理学院,呼和浩特010018 [2]内蒙古自治区应用数学中心,呼和浩特010022 [3]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《应用数学和力学》2023年第7期825-833,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11962026,12002175,12162027,62161045);内蒙古自然科学基金项目(2020MS-01018,2021MS01013,2022ZD05,2023QN01007);内蒙古自治区高等学校科学技术研究项目(NJZY22519)。

摘　　要：考虑了立方准晶压电材料的半空间问题.给出了反平面机械载荷和面内电载荷作用下立方准晶压电材料弹性问题的控制方程,结合半无限区域表面边界条件,利用算子理论和复变函数方法获得了立方准晶压电材料半空间问题一般解的表达式.基于一般解得到了集中线力作用下,半空间问题的声子场和相位子场的位移、应力以及电位移的解析表达式.The half space problem of cubic quasicrystal piezoelectric materials was considered.The governing equations of elasticity for cubic quasicrystal piezoelectric materials under anti-plane deformation and in-plane electric field were given.Combined with the surface boundary conditions in the semi-infinite region,a general solution was obtained by means of the operator theory and the complex function method.Then the analytical expressions of the displacements and stresses of the phonon field and the phason field,and the electric displacements of the half space problem under concentrated linear surface forces,were derived.

关 键 词：立方准晶压电材料 复变函数法 半空间 线性力 

分 类 号：O29[理学—应用数学]