Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 51–58 | Cite as

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

  • Qing Guang-hui  (卿光辉)Email author
  • Qiu Jia-jun  (邱家俊)
  • Liu Yan-hong  (刘艳红)


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.

Key words

piezoelectric material smart laminated plate vibration analysis Hamiltonian isoparametric element semi-analytical solution 

Chinese Library Classification

O343.2 O176 

2000 Mathematics Subject Classification

74B99 49S05 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Qing Guang-hui  (卿光辉)
    • 1
    Email author
  • Qiu Jia-jun  (邱家俊)
    • 2
  • Liu Yan-hong  (刘艳红)
    • 1
  1. 1.Aeronautical Mechanics and Avionics Engineering CollegeCivil Aviation University of ChinaTianjinP. R. China
  2. 2.Department of Mechanics and Engineering Measurement, School of Mechanical EngineeringTianjin UniversityTianjinP. R. China

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