Electro-mechanical responses of transversely isotropic piezoelectric nano-plate based on the nonlocal strain gradient theory with flexoelectric effect

Based on the nonlocal strain gradient theory and flexoelectricity theory, a new model of transversely isotropic piezoelectric rectangular nano-plate subjected to a distributed load is proposed. The nonlocal effect, strain gradient effect and flexoelectric effect are all considered in the novel model. The governing equation and different boundary conditions for a clamped nano-plate under closed circuit and open circuit states are derived by Hamilton principle. Based on the new model, the electro-mechanical responses of piezoelectric nano-plate are numerically analyzed. When the dimensionless nonlocal scale coefficient is smaller than 3, both the central deflection and the central electric potential show significant size dependence. The nonlocal effect causes the nano-plate to be softened while the strain gradient effect makes it stiffened. Compared with the piezoelectric effect, the impact of the flexoelectric effect on the central electric potential plays a dominant role. In addition, the electric potential increases from each lateral edge to the center symmetrically, reaching a maximum at the central point. This paper elucidates the competitive relationship among the influencing effects and concurrently discovers that these effects have a comparable magnitude of impact on the electro-mechanical responses of nano-plate.