特殊正交各向异性压电弯曲板的精化理论  

Refined theory of special orthotropic piezoelectric bending plates

作　　者：陈颖[1] 赵宝生[1] 

机构地区：[1]辽宁科技大学机械工程与自动化学院,辽宁鞍山114051

出　　处：《辽宁科技大学学报》2016年第2期130-136,共7页Journal of University of Science and Technology Liaoning

基　　金：国家自然科学基金项目(11472299)

摘　　要：对特殊正交各向异性压电材料进行了精化分析,给出了该材料板弯曲时的精化理论。首先,介绍特殊正交各向异性压电材料满足的基本方程和通解,并将调和函数的算子函数表示推广到椭圆广义调和函数。其次,利用算子函数表示将板内的位移场、电势场、应力场和电位移场利用二维函数表示出来。然后,利用非齐次边界条件,获得该板在作用横向载荷时的精化方程。最后,对精化方程进行分析,略去高阶项后,得到了特殊正交各向异性压电弯曲板作用横向载荷时的近似方程。由于该研究方法没有进行预先假设,所以获得的结果比一般的板变形理论更精确。In this paper,the special orthotropic piezoelectric material is analyzed,and the refined theory of special orthotropic piezoelectric plate is obtained. Firstly,the fundamental equations and general solutions are introduced,and the operator functions of elliptical general harmonic functions are gained basing on the operator functions of harmonic functions. Secondly,by using the operator functions of elliptical general harmonic functions,the displacement field,electric potential field,stress field and electric displacement field of the plates are expressed by two dimensional operator function. Thirdly,the refined equations of the plates with transverse load are obtained basing on non-homogeneous boundary conditions. Finally,the approximate equations of the special orthotropic piezoelectric bending plates with transverse load are derived by omitting the high-order items. The refined theory provides the solutions of special orthotropic piezoelectric plate without ad hoc assumptions,and this result is more precisely than results by using other theory of elastic plates.

关 键 词：特殊正交各向异性 压电板 精化理论 Lur’e方法 

分 类 号：O343[理学—固体力学]