Bending of a sinusoidal piezoelectric nanoplate with surface effect

The bending problem of a simply supported piezoelectric nanoplate with surface effect is analyzed via the sinusoidal plate model. The piezoelectric nanoplate is treated as a bulk core plus two surface layers. The effect of the surface piezoelectricity on the effective property of the plate system is modeled by a spring force exerting on the boundary of the bulk core. The governing equations are derived by the variational principle. The effect of the surface effect and electric loading on the displacement, electric potential, stress and electric displacement are numerically presented and some new features are observed which should be of particular interest to the future analysis on nanoplates.