功能梯度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 a Functionally Graded Piezoelectric Hollow Cylinder

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：《力学季刊》2005年第1期134-143,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目资助(10272081)

摘　　要：圆环形的压电材料器件在智能结构中得到了广泛的应用。本文推导了横观各向同性功能梯度压电材料圆环在内、外边界上给定位移和电势情况下的一般解。极化方向在圆环的半径方向,材料常数的梯度方向也设定在半径方向,并可表示为半径r 的幂,本构关系为线性。然后推导了压电圆环外壁固定、接地,内壁沿垂向有一微小位移、电势分别为余弦分布和均匀分布的问题的精确解,并计算了该问题在这两种电势情况下产生的无量纲形式的径向和环向位移、电势、应力及电位移沿径向分布的数值结果。计算中考虑了不同的材料梯度,以及内壁的位移与电势的不同比例。This paper provides with a general solution for a hollow cylinder made of a transversely isotropic and functionally graded piezoelectric material, polarized in the radial direction. The displacement and electric potential are prescribed on the outer and inner boundaries. The linear constitutive law is employed in the solution. The material properties are assumed to be proportional to r t, where r is the distance of the material point to the axis of the cylinder, and t is a known constant. The exact solutions are obtained for two sample problems that the outer boundary is fixed and grounded, and the inner boundary has a downward constant small displacement and non-zero electric potentials with, respectively, cosine function distribution and uniform distribution. Numerical results for distributions of dimensionless displacement, electric potential, stresses and electric displacement across the thickness of the cylinder are given. These data may be useful for analyzing some piezoelectric components in smart structures..

关 键 词：横观各向同性 功能梯度压电材料 圆环 精确解 

分 类 号：O343.1[理学—固体力学]