Hamiltonian parametric element and semi-analytical solution for smart laminated plates  

作　　者：卿光辉 邱家俊 刘艳红 

机构地区：[1]Aeronautical Mechanics and Avionics Engineering College, Civil Aviation University of China, Tianjin 300300, P. R. China [2]Department of Mechanics and Engineering Measurement, School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China [3]Aeronautical Mechanics and Avionics Engineering College,Civil Aviation University of China, Tianjin 300300, P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第1期51-58,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10072038)

摘　　要：Based on the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows： the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.Based on the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows： the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.

关 键 词：piezoelectric material smart laminated plate vibration analysis Hamilto-nian isoparametric element semi-analytical solution 

分 类 号：O343.2[理学—固体力学] O176[理学—力学]