Size-dependent bending and vibration behaviors of piezoelectric circular nanoplates

The size-dependent bending and vibration behaviors of a clamped piezoelectric circular nanoplate are investigated by using a modified Kirchhoff plate model. The flexoelectricity, the surface effect and the non-local elastic effect are taken into account in the modified model by decomposing the electric Gibbs free energy into the bulk and surface parts and including the strain gradient and the electric field gradient terms into the bulk energy density function. Different from the results predicted by the classical plate model, the proposed model predicts size-dependent behaviors of the piezoelectric thin plate with nanoscale thickness. Comparisons among the models considering the flexoelectricity, the surface effect and the non-local elastic effect individually, the current model and the classical model are also given in this study. Simulation results indicate that the electromechanical coupling properties, the transverse displacements and the resonant frequencies of the plate are significantly influenced by each individual effect as well as their combined effects. It is also indicated that such effects are affected by the external applied electric potential and the plate geometries. Neglecting any individual effect may induce inaccurate characterization of the electromechanical coupling of the piezoelectric nanoplate. Therefore, the current plate model is expected to provide more accurate predictions of the electromechanical coupling and the mechanical behaviors of piezoelectric circular nanoplate-based devices in the nanoelectromechanical systems.