Research Article
Thermoelastic and Pyroelectric Couplings Effects on
Dynamics and Active Control of Smart Piezolaminated Beam
Modeled by Finite Element Method
M. Sanbi,
1
R. Saadani,
2
K. Sbai,
2
and M. Rahmoune
2
1
Team Science and Advanced Technologies, National School of Applied Sciences, Abdelmalek Essaadi University,
93030 Tetouan, Morocco
2
Team Advanced Materials and Energy Systems, High School of Technology, Moulay Ismail University, 50040 Meknes, Morocco
Correspondence should be addressed to M. Rahmoune; rahmoune@umi.ac.ma
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. Tis 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 fnite element approximations. Te structure consists of a modeling of cantilevered piezolaminated Timoshenko beam
with integrated thermopiezoelectric elements between two aluminium layers. Te 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.
Te optimal control LQG accompanied by the Kalman flter is applied. Te efects 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.
1. Introduction
In the development of distributed sensors, actuators, and
thin-flm devices, thin layer piezoelectrics (either laminated,
deposited, or embedded) are of importance in many appli-
cations, for example, dynamic measurement, control, actu-
ation, and so forth. In case studies of electromechanical
coupling and implementation of the fnite element method,
several studies have been the subject of research on the
topic covered in this paper. Aldraihem and Khdeir [1] have
studied smart beams with extension and thickness-shear
piezoelectric actuators. Trindade et al. [2] have investigated
the piezoelectric active vibration control of damped sandwich
beams. Gabbert et al. [3] have implemented the modeling,
control, and simulation of piezoelectric smart structures
using fnite element method and optimal LQ control. Raja et
al. [4] have analysed the active vibration control of composite
sandwich beams with piezoelectric extension-bending and
shear actuators. Moita et al. [5] have studied the active control
of adaptative laminated structures with bonded piezoelectric
sensors and actuators. Manjunath and Bandyopadhyay have
used the technique of fast output sampling feedback in the
control of vibrations in SISO based Timoshenko structures
[6, 7]. Trindade and Benjeddou [8] have evaluated and opti-
mized the efective electromechanical coupling coefcients of
piezoelectric adaptive structures.
Besides mechanical and electric couplings and interac-
tions, temperature can also infuence the performance of
piezoelectric devices and its variation can introduce volt-
age/charge generation in piezoelectric sensors. In addition,
control voltage can cause temperature rise in piezoelectric
actuators. Temperature can introduce the pyroelectric efect
and the thermal strain efect to the distributed sensors and
also thermal defection in dynamic oscillations. Aouadi [9]
Hindawi Publishing Corporation
Smart Materials Research
Volume 2014, Article ID 145087, 10 pages
http://dx.doi.org/10.1155/2014/145087