柱面受温度载荷的轴对称横观各向同性压电热弹性圆柱的精化理论  

A refined theory of axisymmetric piezothermoelastic circular cylinder with transversely isotropic under temperature load

作　　者：吴迪[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,鞍山114051

出　　处：《应用力学学报》2014年第2期282-287,316,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11172319)

摘　　要：将精化理论的研究方法推广到轴对称横观各向同性压电热弹性圆柱的研究中,利用压电热弹性问题的轴对称通解以及准调和函数的Bessel算子函数表示方法,获得了该圆柱在柱面受温度载荷作用下的精确耦合场;当柱面受到随轴向Z增大而逐渐减小的轴对称量纲为一的温度载荷时,绘制出圆柱在半径r分别为0.2、0.4、0.6、0.8、1.0时的位移分量、电势、温度增量沿轴向z的分布。结果表明:圆柱在同一高度的情况下,径向位移和轴向位移随半径增大而增大,电势的绝对值也随半径的增大而增大,而温度增量随半径的变化则不明显。此外,本文还通过算例验证了该精化理论应用的正确性。Most of research on mechanical properties of piezothermoelastic materials rarely starts with foundation models, but to add thermal and electric coupled term in classical mechanics research results. Thus the results obtained are approximate. If they are applied to the analysis of micro structure directly, it will bring great error. By using the refined theory, the exact coupled fields are obtained without employing any assumptions. Research of refined theory is extended to the study of axisymmetric piezothermoelastic circular cylinder with transversely isotropic. The coupled fields of the circular cylinder which is suffered from axisymmetric temperature load are given by using Bessel's function and the general solutions of the axisymmetric piezothermoelastic problem. For a given temperature load, the displacements components, potential and temperature increment distributions of the circular cylinder under different radius r = 0.2, 0.4, 0.6, 0.8 and 1.0 are mapped which are along the axial direction z. It turned out that at the same height, the increasing radius bring larger radial and axial displacement. Moreover, the absolute value of potential increases with the radius increasing, but the changes in temperature increment over radius are not obvious. For illustrating the applications of the exact theory, an example is presented.

关 键 词：轴对称圆柱 压电热弹性材料 横观各向同性 精化理论 BESSEL函数 

分 类 号：O343[理学—固体力学]