Analysis of surface effect and flexoelectric effect on the electromechanical responses of bilayered transversely isotropic rectangular micro-plate

A new model of a bilayered transversely isotropic piezoelectric rectangular micro-plate with a distributed load is developed on the basis of Kirchhoff's plate theory and the extended linear piezoelectricity theory to characterize the piezoelectric micromachined ultrasonic transducer. The model takes into account both the surface effect and the flexoelectricity effect. The governing equation at the simply supported boundary condition is derived according to the variation principle. Based on the new model, the size dependent electromechanical coupling behaviors of the bilayered piezoelectric rectangular micro-plate are investigated. Considering the flexoelectric effect and surface effect synchronously, the numerical result indicates that the size dependence of the normalized central deflection decreases as the residual surface stress increases. For negative residual stress, the surface effect is the main influencing factor. While for positive residual stress, the surface effect dominates only when the ratio of thickness to length is smaller than about 25; otherwise, the flexoelectric effect will be more crucial. Moreover, if the thickness of the piezoelectric layer is less than about 40 nm, the electrical potential and polarization show a stronger size dependence. These results will be helpful to design and manufacture a piezoelectric micromachined ultrasonic transducer.