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

• Published in: Applied mathematics and mechanics Vol. 28; no. 1; pp. 51 - 58
• Main Author: 卿光辉 邱家俊 刘艳红
• Format: Journal Article
• Language: English
• Published: Aeronautical Mechanics and Avionics Engineering College,Civil Aviation University of China, Tianjin 300300, P. R. China%Department of Mechanics and Engineering Measurement, School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China 2007
• Subjects: Boundaries; Cantilever plates; Laminates; Mathematical analysis; Mathematical models; Piezoelectricity; Plates; Vibration; 半解析解; 各向异性压电材料; 振动分析; 智能层合扳; 汉密尔顿等参元; vibration analysis; smart laminated plate; piezoelectric material; Hamiltonian isoparametric element; semi-analytical solution
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-007-0106-z

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.