压电材料圆环位移和电势边值问题的精确解  

Exact Solutions of Displacement and Electric Potential Boundary Value Problems for Piezoelectric Hollow Cylinders

作　　者：杨昌锦[1] 李尧臣[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《同济大学学报（自然科学版）》2005年第10期1342-1346,共5页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10272081)

摘　　要：采用在半径方向有极化时的横观各向同性的线性本构关系,对压电材料圆环在给定位移边界条件和电势边界条件的情况下,得出了问题的一般解.推导了外壁固定、接地,内壁沿垂直方向有一微小位移,内壁上电势为均匀分布问题的精确解.计算了该问题的量纲一位移、电势、应力、电位移沿径向变化的数值结果,并将差分解和精确解的结果进行了比较.With the use of a linear constitutive relation for a transversely isotropic piezoelectric hollow cylinder poled in the radial direction, this paper gives a general solution for the problem in which the displacement and electric potential boundary conditions are properly defined. The exact solutions are obtained for the problem that the outer boundary is fixed and grounded, and the inner boundary has a downward constant small displacement and non-zero electric potential with uniform distribution. Nu-merical results for distributions of displacements, electric displacements, electric potential and stresses across the thickness of the hollow cylinder are given in a dimensionless form. These data may be useful for analyzing some piezoelectric components in smart structures.

关 键 词：横观各向同性 压电材料 圆环 精确解 

分 类 号：TB381[一般工业技术—材料科学与工程]