Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate

Flexoelectricity, referring to the coupling between electric polarization and strain gradients, is a universal effect in all dielectrics and may become manifest at the nano-scale. The current work aims to investigate the flexoelectric effect on the electroelastic responses and the free vibrational behaviors of a piezoelectric nanoplate (PNP). Based on the conventional Kirchhoff plate theory and the extended linear piezoelectricity theory, the governing equation and the boundary conditions of a clamped PNP with the consideration of the static bulk flexoelectricity are derived. Ritz approximate solutions of the electroelastic fields and the resonant frequencies demonstrate the size-dependency of the flexoelectric effect, which is more prominent for thinner plates with smaller thickness as expected. Simulation results also indicate that the influence of the flexoelectricity upon the electroelastic fields of a bending PNP and the transverse vibration of the PNP is sensitive to the plate in-plane dimensions as well as the applied electric voltage. Moreover, it is suggested that the possible frequency tuning of a PNP resonator by adjusting applied electrical load warrants the consideration of the flexoelectricity. This study is claimed to provide a theoretical predicition on the trend of the flexoelectric effect upon the static and dynamic behaviors of a bending PNP, thus sheding light on understanding the underlying physics of electromechanical coupling at the nano-scale to some extent.