立方准晶压电材料的半空间问题

李光芳; 刘昉昉; 于静; 李联和

doi:10.21656/1000-0887.430221

立方准晶压电材料的半空间问题

doi: 10.21656/1000-0887.430221

李光芳^{1, 2,},
刘昉昉^{2, 3},
于静²,
李联和^{2, 3, ,}

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

基金项目:

国家自然科学基金项目 11962026

国家自然科学基金项目 12002175

国家自然科学基金项目 12162027

国家自然科学基金项目 62161045

内蒙古自然科学基金项目 2020MS-01018

内蒙古自然科学基金项目 2021MS01013

内蒙古自然科学基金项目 2022ZD05

内蒙古自然科学基金项目 2023QN01007

内蒙古自治区高等学校科学技术研究项目 NJZY22519

详细信息

作者简介:
李光芳(1989—)，女，讲师，硕士(E-mail: liguangfang@126.com)

通讯作者:
李联和(1978—)，男，教授，博士，博士生导师(通讯作者. E-mail: nmglilianhe@163.com)

中图分类号: O29
计量
- 文章访问数: 229
- HTML全文浏览量: 112
- PDF下载量: 63
- 被引次数: 0
出版历程
- 收稿日期: 2022-07-04
- 修回日期: 2022-10-24
- 刊出日期: 2023-07-01

The Half Space Problem of Cubic Quasicrystal Piezoelectric Materials

LI Guangfang^{1, 2
,},
LIU Fangfang^{2, 3},
YU Jing²,
LI Lianhe^{2, 3
, ,}

1.
College of Science, Inner Mongolia Agricultural University, Hohhot 010018, P.R.China
2.
Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China
3.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China

摘要

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.
- 立方准晶压电材料 /
- 复变函数法 /
- 半空间 /
- 线性力
Abstract: 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.
- cubic quasicrystal piezoelectric material /
- complex function method /
- half space /
- linear force

HTML全文

图 1 力电载荷作用下的半无限区域

Figure 1. The semi-infinite region under electromechanical load

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图 2 无量纲声子场位移$ \bar{u}_z$等势图

Figure 2. The contour of dimensionless phonon field displacement $ \bar{u}_z$

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图 3 无量纲相位子场位移$ \bar{w}_z$等势图

Figure 3. The contour of dimensionless phason field displacement $ \bar{w}_z$

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图 4 无量纲电势Φ等势图

Figure 4. The contour of dimensionless potential Φ

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