压电/压磁复合楔形结构耦合场的奇异性研究：反平面问题

王国林; 温建俊; 岳彦美; 刘金喜

doi:10.21656/1000-0887.450244

压电/压磁复合楔形结构耦合场的奇异性研究：反平面问题

doi: 10.21656/1000-0887.450244

王国林^{1, 2,},
温建俊²,
岳彦美³,
刘金喜^{1, 3, ,}

1.
石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室，石家庄 050043
2.
石家庄铁道大学土木工程学院，石家庄 050043
3.
石家庄铁道大学工程力学系，石家庄 050043

基金项目:

国家自然科学基金 11272222

河北省高等学校科学技术研究项目 QN2020204

详细信息

作者简介:
王国林(1990—)，男，实验师，博士(E-mail: wangglstdu@163.com)

通讯作者:
刘金喜(1961—)，男，教授，博士，博士生导师(通讯作者. E-mail: liujx02@hotmail.com)

中图分类号: O343
计量
- 文章访问数: 187
- HTML全文浏览量: 64
- PDF下载量: 42
- 被引次数: 0
出版历程
- 收稿日期: 2024-09-06
- 修回日期: 2024-09-25
- 刊出日期: 2024-10-01

Singularities of Coupled Fields in Piezoelectric/Piezomagnetic Composite Wedges: an Antiplane Problem

WANG Guolin^{1, 2
,},
WEN Jianjun²,
YUE Yanmei³,
LIU Jinxi^{1, 3
, ,}

1.
State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R.China
2.
School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R.China
3.
Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R.China

摘要

摘要: 研究了反平面变形状态下压电/压磁复合楔形结构耦合场的奇异性. 应用复变函数理论和本征函数展开方法，推导了16种机械、电学和磁学组合边界条件下关于奇异性指数本征方程的显函表达式. 基于得到的本征方程，通过数值算例表明了楔角、边界条件和材料组合类型对耦合场奇异性的影响，发现压电效应和压磁效应之间的相互作用导致压电/压磁复合楔磁电弹场的奇异性比压电复合楔电弹场的奇异性更加复杂.
- 压电材料 /
- 压磁材料 /
- 复合楔形结构 /
- 反平面变形 /
- 耦合场 /
- 奇异性指数
Abstract: The singularities of the coupled fields near the apex of a piezoelectric/piezomagnetic composite wedge under antiplane deformation were studied. With the complex variable function theory and the eigenfunction expansion method, the explicit expressions of the eigenfunction equations for singularity orders were derived for 16 combinations of mechanically free or clamped, electrically closed or open and magnetically closed or open ones. Based on the obtained eigenequations, some numerical results were given to show the influences of the wedge angles, boundary conditions and material combination types on the singular behaviors. The results show that, the singularities of the coupled fields in a piezoelectric/piezomagnetic composite wedge are more complicated than those in a piezoelectric counterpart.
- piezoelectric material /
- piezomagnetic material /
- composite wedge /
- anti-plane deformation /
- coupled field /
- singularity order

HTML全文

图 1 层状磁电复合材料及楔形结构模型

Figure 1. Layered magnetoelectric composites and the wedge model

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图 2 压电/压磁复合楔形结构

Figure 2. A piezoelectric (PE)/ piezomagnetic (PM) composite wedge

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图 3 电学开路/磁学短路(FD/FB)边界下，BTO/CFO和PZT-4/CFO楔的奇异性

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. The singularity orders for BTO/CFO and PZT-4/CFO wedges with boundary condition combination FD/FB

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图 4 电学开路/磁学开路(FD/FH)边界下，BTO/CFO和PZT-4/CFO楔的奇异性

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. The singularity orders for BTO/CFO and PZT-4/CFO wedges with boundary condition combination FD/FH

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图 5 电学开路/磁学短路(FD/FB)边界下，BTO/CFO和BTO/TFD楔的奇异性

Figure 5. The singularity orders for BTO/CFO and BTO/TFD wedges with boundary condition combination FD/FB

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图 6 电学开路/磁学开路(FD/FH)边界下，BTO/CFO和BTO/TFD楔的奇异性

Figure 6. The singularity orders for BTO/CFO and BTO/TFD wedges with boundary condition combination FD/FH

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图 7 机械固支-电学开路和机械自由-磁学开路(CD/FH)边界下，BTO/CFO楔的奇异性

Figure 7. The singularity orders for the BTO/CFO wedge with boundary condition combination CD/FH

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图 8 机械自由、电学开路和磁学开路(FD/FH)边界下，力磁耦合对BTO/CFO楔奇异性的影响

Figure 8. The effect of magnetomechanical coupling on the singularity orders of the BTO/CFO wedge under the FD/FH boundary

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图 9 机械自由、电学开路和磁学短路(FD/FB)边界下，PZT-4/CFO楔最强奇异性指数随楔角α和β的变化

Figure 9. Variations of the strongest singularity orders of the PZT-4/CFO wedge under boundary condition combination FD/FB with wedge angles α and β

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图 10 机械自由、电学开路和磁学开路(FD/FH)边界下，PZT-4/CFO楔最强奇异性指数随楔角α和β的变化

Figure 10. Variations of the strongest singularity orders of the PZT-4/CFO wedge under the boundary condition combination FD/FH with wedge angles α and β

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表 1 材料常数

Table 1. Material constants

parameter	BTO^[43]	PZT-4^[44]	CFO^[43]	TFD^[45]
c₄₄/(10¹⁰·N/m²)	4.3	2.56	4.53	0.599
e₁₅/(C/m²)	11.6	12.7	-	-
ε₁₁/(10^－9·C²/(N·m²))	11.2	6.46	-	-
h₁₅/(N/(A·m))	-	-	550	167.66
μ₁₁/(10^－6·N·S²/C²)	-	-	590	3.98

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