横观各向同性压电功能梯度旋转圆盘的三维解析解  

3D Analytical Solution for Rotating Disc of Functionally Graded Piezoelectric Materials with Transversely Isotropy

作　　者：翁国飞[1] 刘麟闻[1] 陈江瑛[1] 

机构地区：[1]宁波大学机械工程与力学学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2009年第3期390-395,共6页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(10472102);宁波大学人才基金(2006931);宁波大学王宽诚基金

摘　　要：从横观各向同性压电弹性力学轴对称问题基本方程出发,采用直接位移法将位移分量展开成径向坐标r的幂函数线性组合形式,其中含有7个待定的位移函数,它们是坐标z的函数,由基本方程导出关于位移函数的控制方程,结合相应的边界条件,可以积分得到位移函数,并确定积分常数,从而给出横观各向同性压电功能梯度旋转圆盘的三维解析解.并通过相应算例展示了一种特殊形式的压电功能梯度材料的梯度指标对应力场、位移场和电场的影响.Based on the basic equations of axisymmetric problems identified with transversely isotropic piezoelectric materials, the displacement components are expanded and assumed to fit with polynomials of the radial coordinate with seven involved parameters, resulting with seven undetermined displacement functions in the thickness coordinate. The displacement can be obtained through integration along with the consideration of the boundary conditions of the disc. Thus a three-dimensional analytical solution is attained for the piezoelectric rotating disc made of transversely isotropic and functionally graded materials, in which the material properties are the arbitrary functions of the thickness coordinate. The effect of gradient index on the field of stress, displacement and electricity is demonstrated through presenting a special functionally graded piezoelectric material.

关 键 词：旋转圆盘 三维解析解 压电功能梯度材料 横观各向同性 

分 类 号：O343[理学—固体力学]