基于Hamilton理论的压电材料智能叠层板的固有频率分析  

Natural frequencies analysis of piezoelectric laminated plates in Hamiltonian system

作　　者：刘艳红[1,2] 张惠明[1] 卿光辉[2] 

机构地区：[1]天津大学内燃机燃烧学国家重点实验室,天津300072 [2]中国民航大学航空工程学院,天津300300

出　　处：《船舶力学》2009年第5期788-794,共7页Journal of Ship Mechanics

基　　金：国家自然科学基金(50276041);中国民航大学科研基金(CAUCNo.05YK07M)

摘　　要：根据压电材料修正后的Hellinger-Reissner(H-R)变分原理,推导了各向异性压电材料Hamiltonian等参元的一般形式,应用该等参元分析了具有机电耦合效应的正交异性叠层板的自由振动问题。首先将叠层板的压电层和主体层看作独立的三维体,应用Hamiltonian等参元离散各层,分别建立了各层的方程;考虑到主体层和压电层连接界面上广义应力和广义位移的连续性,联立两者的方程得到整体结构的控制方程。以四边固支的矩形叠层板为例进行了的数值分析,并与有关文献的结果进行了比较。Based upon the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified Hamiltonian isoparametric element for the anisotropic piezoelectric material is derived,and the isoparametric element is employed to analyze the anisotropic laminated plate with mechanical-electric coupling effect. Firstly, the piezoelectric layer and host layer of laminated plate are considered as absolute three-dimensional bodies and discretized by the same isoparametric elements. Then the control equation of whole structure is established by considering the compatibility of generalized displacements and generalized stresses on the interface between two layers.The numerical example of rectangular lamina with four edges clamped is analyzed in this paper and the results are compared with the related reference.

关 键 词：压电材料 智能叠层板 Hamilton理论 等参元 半解析法 

分 类 号：TB330.1[一般工业技术—材料科学与工程]