Table of Contents
Smart Materials Research
Volume 2014, Article ID 145087, 10 pages
Research Article

Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

1Team Science and Advanced Technologies, National School of Applied Sciences, Abdelmalek Essaadi University, 93030 Tetouan, Morocco
2Team Advanced Materials and Energy Systems, High School of Technology, Moulay Ismail University, 50040 Meknes, Morocco

Received 19 July 2014; Revised 13 October 2014; Accepted 27 October 2014; Published 24 November 2014

Academic Editor: Marcelo A. Trindade

Copyright © 2014 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.


Smart structures with integrated sensors, actuators, and control electronics are of importance to the next generation high-performance structural systems. In this study, thermopiezoelastic characteristics of piezoelectric beam continua are studied and applications of the theory to active structures in sensing and optimal control are discussed. Using linear thermopiezoelastic theory and Timoshenko assumptions, a generic thermopiezoelastic theory for piezolaminated composite beam is derived. Finite element equations for the thermopiezoelastic media are obtained by using the linear constitutive equations in Hamilton's principle together with the finite element approximations. The structure consists of a modeling of cantilevered piezolaminated Timoshenko beam with integrated thermopiezoelectric elements between two aluminium layers. 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 accompanied by the Kalman filter is applied. The effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. We show that the control procedure cannot be perturbed by applying a thermal gradient and the control can be applied at any time during the period of vibration of the beam.