Nonlinear electro-mechanical responses of functionally graded piezoelectric beams

This study presents analyses of the nonlinear electro-mechanical responses of functionally graded piezoelectric beams undergoing small deformation gradients. The studied functionally graded beams comprise of electro-active and inactive constituents with gradual compositions varying through the thickness of the beams. Two types nonlinear electro-mechanical responses are considered for the active constituents, which are nonlinear electro-mechanical behaviors for the polarized piezoelectric constituent under electric fields smaller than the coercive limit, and polarization switching responses due to cyclic electric fields with high amplitude. The inactive constituent is modeled with uncoupled linear electro-elastic response. The functionally graded beam is discretized into several graded layers through its thickness. Each layer is comprised of different compositions of the active (piezoelectric) inclusions and conductive matrix. A particle-unit-cell micromechanical model is used to obtain the nonlinear electromechanical responses in each layer and is integrated within the laminate theory in order to obtain the overall nonlinear electro-mechanical responses of the functionally graded piezoelectric beams. The numerical predictions are compared with experimental data available in literature. Parametric studies are then performed in order to examine the effects of the thickness of the beam, of the concentration of the constituent, and the frequency of the cyclic electric field on the overall electro-mechanical response of the functionally graded piezoelectric beams.