基于高阶板理论的有限单元及其在压电智能结构中的应用研究  

On the Finite Element Based on the Refined Higher Order Plate Theory and Its Applications to Piezoelectric Smart Structures

作　　者：周勇[1] 王鑫伟[1] 于四海[2] 

机构地区：[1]南京航空航天大学智能材料与结构航空科技重点实验室,南京210016 [2]解放军理工大学理学院,南京210016

出　　处：《机械科学与技术》2004年第8期950-953,956,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目 ( 10 0 72 0 2 6);国家自然科学基金项目 ( 5 0 13 5 0 3 0 )资助

摘　　要：带有分布式压电驱动器 /传感器的自适应智能材料结构在振动控制、形状控制、精确定位等方面具有很大潜力而受到广泛的关注。本文把x ,y方向的位移定义为厚度坐标的三次多项式 ,利用板上下自由表面的力边界条件及正交异性复合材料的特性 ,导出了改进的高阶板理论。依据该理论建立了 4节点 2 0自由度矩形板高阶有限单元 ,并对一些算例进行了分析。通过与文献结果的对比 ,验证了改进的高阶板理论和所建立单元的正确性。最后利用所建立的单元 ,分析了压电悬臂梁中压电层在不同脱胶长度情况下板的频率变化 。Recently, attention has been paid to the adaptive composite structures with distributed piezoelectric actuators and sensors due to their potentiality in a wide range of applications such as vibration suppression, shape control and precision positioning. In this paper, the displacement components in the x,y directions, u,v, at an arbitrary point in a laminate plate are defined as a third order polynomial of thickness coordinate z. Applying the orthotropic composite properties and the free force boundary conditions on the plate surfaces, a refined higher order plate theory is presented. Based on the theory; a 4-node-20-degree-of-freedom rectangular finite element is developed. Several benchmarks tests are carried out. Numerical results agree well with the existing data in the literatures, thus the accuracy of the refined theory and the proposed element are verified. At the end of the paper, the effects of the different piezoelectric debonding length on the natural frequency of the smart plate are analyzed by using the proposed finite element. Results agree well with the experimental data.

关 键 词：复合材料 压电智能结构 脱胶 有限元 

分 类 号：TH165.3[机械工程—机械制造及自动化]