Electro-mechanical responses of flexoelectric bilayer circular nano-plate with surface effect

Based on the theory of flexoelectricity in elastic dielectrics and the principle of minimum potential energy, a new theoretical model of bilayer circular nano-plate containing a piezoelectric layer is constructed. This model is used to analyze the effects of external loading, applied voltage, flexoelectric effect, and surface effect on the bending deflection, polarization, and normalized electric potential of the nano-plate. Numerical results indicate that external loading and applied voltage have opposite effects on the radial deflection of the bilayer circular nano-plate, with external loading having a more significant influence on deflection than the flexoelectric effect. Applied voltage also affects the normalized electric potential of the bilayer nano-plate. In the presence of negative surface residual stress, the deflection is mainly influenced by the flexoelectric effect. When the surface residual stress is positive and the ratio of radius to thickness is less than 25, the surface effect dominates the deflection behavior. Additionally, the positive or negative surface residual stress leads to an increase or decrease in polarization. The results provide a theoretical basis for the design of intelligent components containing piezoelectric bilayer circular nano-plates.