压电/压磁复合楔形结构耦合场的奇异性研究:反平面问题  

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

作　　者：王国林 温建俊 岳彦美 刘金喜[1,3] WANG Guolin;WEN Jianjun;YUE Yanmei;LIU Jinxi(State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;Department of Engineering Mechanics,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2024年第10期1256-1267,共12页Applied Mathematics and Mechanics

基　　金：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)。

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.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.

关 键 词：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 

分 类 号：O343[理学—固体力学]