基于高阶位移模式的压电层合板动力有限元模型  

Finite element model for dynamics of laminated piezoelectric plates based on higher order theory

作　　者：王锋[1] 李道奎[1] 唐国金[1] 

机构地区：[1]国防科技大学航天与材料工程学院,长沙410073

出　　处：《计算力学学报》2007年第6期892-898,共7页Chinese Journal of Computational Mechanics

基　　金：国家863基金(2002AA001006)资助项目

摘　　要：建立了含压电片层合板的有限元动力学模型。以位于压电层上下表面处的电场强度和层间电压为未知量,给出了三次函数的电势分布模式,采用Reddy的高阶剪切理论描述板的位移场,假设板厚度方向的正应力为零给出了减缩的本构方程,采用有限元方法,基于Hamilton原理导出结构的动力学方程,然后用静态缩聚的方法压缩掉电场自由度和次要的位移自由度。最后用四边形矩形单元求解了一对称铺层和非对称铺层悬臂板的固有频率,并与ANSYS结果对比验证了本文模型的精确性。The element model for dynamics of composite laminates containing distributed piezoelectric sheets is formulated. A new electric potential model is presented with a set of cubic polynomials, which takes electric intensity at the top and bottom surfaces and voltage between the interfaces of a piezoelectric lamina as unknown coefficients. And Reddy＇s higher order plate theory is adopted to model the displacement fields. The reduced constitutive equation is deduced based on the assumption that the normal stress of the plate is zero. With the finite element method the dynamical equations is derived from the Hamilton variational principle. Then, the electric intensity freedoms and secondary displacement freedoms are eliminated using static condensation method. Finally, four-node rectangular element is implemented for the frequency analysis of a symmetrically layered and a unsymmetrically layered clamped rectangular plate, and the results are compared to that of ANSYS software using solid elements to validate the presented model.

关 键 词：压电结构 层合板 电势分布模型 有限元方法 

分 类 号：TU313.3[建筑科学—结构工程] O328[理学—一般力学与力学基础]