INTRODUCTION
1.3 Smart structures
1.3.1 Smart FG structures
The FG materials have several advantages over the convectional composites and hence find their wide applications especially for aerospace structures. The aerospace structures are generally lightweight flexible structures and always require advanced structural design that could be achieved through the use of the concept of smart structure. So, the concept of smart structure is extensively employed for designing similar flexible FG structural components. If an FG structure is integrated with piezoelectric sensor and/or actuator patches for achieving its self-sensing and/or self-controlling capabilities, then the overall FG structure may be called as smart FG structure. A great deal of research has already been carried out on this topic and also reported in the literature. Wang and Noda (2001) presented an analysis of a smart FG structure using piezoelectric distributed actuator and found that the smart actuator could control both the stress and thermal deformation effectively. Ootao and Tanigawa (2001) studied the performance of a piezoelectric actuator for controlling the transient thermo-elastic displacements of FG plates. Chen et al. (2002) developed a three-dimensional theory for free vibration analysis of smart FG rectangular plates.
Liew et al. (2003) performed the static and dynamic analyses of smart FG plates under a temperature gradient, and determined the optimum configurations of the piezoelectric sensor/actuator pairs for effective control of FG plates under various thermal as well as mechanical loads. Zhong and Shang (2003) derived three- dimensional exact solutions for a simply-supported smart FG plate, and studied the influences of the different FG material properties on the structural response of the plate to the mechanical and electric stimuli. Liew et al. (2003) developed a finite element model for the static and dynamic pizeo-thermo-elastic analyses of smart FG plates under thermal environment. This work presents the effects of the constituent- volume fractions and the influence of feedback control gain on the static and dynamic responses of the FG plates. Liew et al. (2004) presented numerical results for shape control of FG plates under a temperature gradient by optimizing the voltage distribution for the open-loop control and the displacement control-gain values for
Introduction
12
the closed-loop feedback control. They also carried out similar study of optimal control of FG plates using genetic algorithm (Liew et al. 2004). Altay and Kmeci (2005) derived two-dimensional approximate equations for vibration of FG piezo- electro-magnetic plate. Shen (2005) presented post-buckling analysis for a simply- supported shear deformable FG plate integrated with piezoelectric distributed actuators, where the smart FG plate was considered to be subjected to a combined load of mechanical, electrical and thermal loads. In this study, the effects of temperature-rise, constituent-volume fractions, applied voltage, the character of in- plane boundary conditions as well as initial geometric imperfections on the post- buckling responses of the smart FG plate are studied. Ebrahimi and co-workers (2008, 2009) carried out an analytical investigation on the free vibration behaviour of thin/moderately thick circular FG plates integrated with two uniformly distributed actuator layers made of piezoelectric material (PZT4). This study exhibits effect of variation of the gradient index of FG plate on its free vibration characteristics.
Shakeri and Mirzaeifar (2009) presented a finite element formulation based on layer- wise theory for analysing the quasi-static and free vibration response of smart FG plates to impulse loads. The authors (Shakeri and Mirzaeifar, 2009) showed that the non-linear distribution of electric potential in thick piezoelectric layers could be captured using the proposed model. Xiang and Shi (2009) studied FG-piezoelectric sandwich cantilever plates under an applied electric field and/or a thermal load for finding out the influences of electro-mechanical coupling, FG index and temperature change on the bending behaviour of piezoelectric actuators or sensors. Mehrabadi et al. (2009) presented free vibration analysis of a smart FG circular plate using classical plate theory (CPT). In this work, the phase-volume fractions were varied for different boundary conditions and their effects on the resonant frequencies were studied.
The smart FG structures are usually thin-walled flexible structures embedded with piezoelectric distributed actuators. Since such thin-walled and flexible smart FG structures are prone to undergo large/nonlinear deformations, researchers have already carried out nonlinear static and dynamic analyses of smart FG structures for the purpose of understanding more realistic structural behaviour of the same under thermo-mechanical loads. Yang et al. (2003) presented semi-analytical solutions for large amplitude vibration of rectangular FG laminated plates integrated with
Introduction
13
piezoelectric sensors and actuators. Results of this study illustrate that the normalized frequency of the FG laminated plate is very sensitive to vibration amplitude, out-of-plane boundary support, temperature change, in-plane compression and the side-to-thickness ratio. The same study (Yang et al. 2003) also shows that FG laminated plates change the inherent “hard-spring” characteristic to
“soft-spring” behaviour at large vibration amplitudes. Huang and Shen (2004) analyzed the nonlinear vibration responses of a smart FG plate under the thermal environment. The host FG plate is integrated with piezoelectric layers and the corresponding analysis reveals significant effects of temperature field and constituent-volume fractions of FG substrate on the nonlinear dynamic response of overall smart FG plate. Yang et al. (2004) carried out a nonlinear bending analysis of smart FG plates in the thermal environment using a differential quadrature method.
This analysis addresses nonlinear bending characteristics of smart heated FG plates in regard to the applied actuator-voltage, the constituent-volume fractions and the temperature gradient. Ebrahimi and Rastgoo (2009) presented nonlinear analytical solutions for a circular FG plate coupled with piezoelectric layers. These analytical solutions reveal controlled dynamic characteristics of the smart circular FG plate with respect to the applied actuator-voltage, thermal environment and constituent- volume fractions in FG substrate plate. Ebrahimi and Rastgoo (2009) also carried out similar nonlinear analysis of thin smart circular pre-stressed FG plate to illustrate the control of nonlinear deflections and natural frequencies using high control voltages.
Yiqi and Fuming (2010) analysed the actively controlled/uncontrolled nonlinear dynamic response of a FG plate integrated with piezoelectric layers and demonstrated corresponding influences of mechanical load, electric load, constituent-volume fraction in FG substrate and geometric parameters. Fakhari et al.
(2011) developed a finite element model of smart FG plate for investigating its nonlinear free and forced transient vibration characteristics under thermo-electro- mechanical load. The numerical results in this study illustrate the effects of FG volume fraction exponent, applied voltage to piezoelectric layers, thermal load and vibration amplitude on the nonlinear free/forced vibration characteristics of the smart FG plate. Behjat and Khoshravan (2012) carried out nonlinear static and free vibration analyses of smart FG plates under different sets of mechanical and
Introduction
14
electrical loads. The corresponding numerical results illustrate the effects of material composition and boundary conditions on nonlinear responses of smart FG plates.