Table of Contents
Smart Materials Research
Volume 2015, Article ID 748459, 15 pages
Research Article

Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

1Equipe Sciences et Technologies Avancées, Ecole Nationale des Sciences Appliquées, Université Abdelmalek Essaadi, 93030 Tétouan, Morocco
2Laboratoire d’Etude des Matériaux Avancés et Applications, Faculté des Sciences et Ecole Supérieure de Technologie, Université Moulay Ismail, 50040 Meknès, Morocco

Received 5 December 2014; Revised 2 April 2015; Accepted 3 April 2015

Academic Editor: Weihua Li

Copyright © 2015 M. Sanbi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton’s principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG-Kalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.