A Multi-layer Piezocomposite Model and Application on Controlled Smart Structures

In smart structural applications, multi-layered piezocomposite plates are very common for the study of active control applications. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite plates containing integrated piezoelectric sensors and actuators subjected to electrical and mechanical loadings. The formulation is based on a third order shear deformation theory and Hamilton’s principle. A nine-noded \(C^0\) plate element is implemented for the analysis. The element was developed to include stiffness and the electromechanical coupling of the piezoelectric sensor/actuator layers. The electric potential is assumed to vary linearly through the thickness for each piezoelectric sublayer. The model is validated by comparing with existing results documented in the literature. A displacement and optimal LQR control algorithm is used for the active control of the static deflection and of the dynamic response of the plates with surface bonded piezoelectric sensors and actuators layers or patches. The main aspects of the application of the present model are discussed through a set of numerical examples.