大连理工大学学报
大連理工大學學報
대련리공대학학보
JOURNAL OF DALIAN UNIVERSITY OF TECHNOLOGY
2001年
2期
187-191
,共5页
压电效应%非线性极化/束缚电荷%扭转效应
壓電效應%非線性極化/束縳電荷%扭轉效應
압전효응%비선성겁화/속박전하%뉴전효응
初步探讨了压电体的扭转效应.应用弹性理论、压电理论分析了压电体内的扭转应力及由其所导致的非线性极化状态.由电动力学理论得知,极化将会在空间产生电场.根据电场的等效原理,极化梯度的存在,不仅在压电体表面上产生等效面束缚电荷,在压电体内部同时也会有等效体束缚电荷聚集.从麦克斯韦方程组及矢量分析出发,推导得到了束缚电荷激发的电场所满足的偏微分方程.通过引入静电场的标量位函数,将电场强度的矢量泊松方程转化为位势的椭圆型偏微分方程的诺依曼边值问题.采用有限元法求解得到了束缚电荷产生的电场强度在压电体内及边界上的分布,得到了迥异于线性极化的结果.根据导体在电场中的边界条件分析,有效地在压电体表面布置了检测电极.理论分析结论得到了实验结果的有力支持,并将为单压电体扭矩测量技术奠定基础.
初步探討瞭壓電體的扭轉效應.應用彈性理論、壓電理論分析瞭壓電體內的扭轉應力及由其所導緻的非線性極化狀態.由電動力學理論得知,極化將會在空間產生電場.根據電場的等效原理,極化梯度的存在,不僅在壓電體錶麵上產生等效麵束縳電荷,在壓電體內部同時也會有等效體束縳電荷聚集.從麥剋斯韋方程組及矢量分析齣髮,推導得到瞭束縳電荷激髮的電場所滿足的偏微分方程.通過引入靜電場的標量位函數,將電場彊度的矢量泊鬆方程轉化為位勢的橢圓型偏微分方程的諾依曼邊值問題.採用有限元法求解得到瞭束縳電荷產生的電場彊度在壓電體內及邊界上的分佈,得到瞭迥異于線性極化的結果.根據導體在電場中的邊界條件分析,有效地在壓電體錶麵佈置瞭檢測電極.理論分析結論得到瞭實驗結果的有力支持,併將為單壓電體扭矩測量技術奠定基礎.
초보탐토료압전체적뉴전효응.응용탄성이론、압전이론분석료압전체내적뉴전응력급유기소도치적비선성겁화상태.유전동역학이론득지,겁화장회재공간산생전장.근거전장적등효원리,겁화제도적존재,불부재압전체표면상산생등효면속박전하,재압전체내부동시야회유등효체속박전하취집.종맥극사위방정조급시량분석출발,추도득도료속박전하격발적전장소만족적편미분방정.통과인입정전장적표량위함수,장전장강도적시량박송방정전화위위세적타원형편미분방정적낙의만변치문제.채용유한원법구해득도료속박전하산생적전장강도재압전체내급변계상적분포,득도료형이우선성겁화적결과.근거도체재전장중적변계조건분석,유효지재압전체표면포치료검측전겁.이론분석결론득도료실험결과적유력지지,병장위단압전체뉴구측량기술전정기출.
The concept of the torsional effect of piezoelectrics is firstproposed in this article. The stresses caused by the mechanical torque on the piezoeletric bar are deduced by using the energy method in the elastic theory and the accompanying non-linear polarization in the piezoelectric body is analyzed. In the viewpoint of electrodynamics, the equivalent bound volume charges will accumulate in the piezoelectric body in addition to the bound surface charges considering the effect of the polarization gradient. The vectorial partial differential equation which the electric field intensity satisfies is deduced by applying Maxwell equations to the situation considered. And the problem is converted to the typical Neumann boundary value problem for the elliptic equations by inducing the scalar potential function.The distribution of the electric field intensity in the piezoelectric body is obtained by the finite element method. The measuring electrodes are effectively disposed on the surfaces of the piezoelectric body based on the analysis of the boundary condition of conductors in the electric field. The investigation in this article would establish the basis for the torque measuring technique on the single piezoelectric body.