Two-dimensional theory of piezoelectric plates considering surface effect

Two-dimensional (2D) equations of piezoelectric plates with nano-thickness are obtained, which take account of the surface effect. The piezoelectric plate is treated as a bulk core plus two surface layers. The influence on the plateʹs overall properties resulted from the surface piezoelectricity is modeled by a spring force exerting on the boundary of the bulk core. Using the derived 2D equations, the Miller–Shenoy coefficients and the natural frequencies of the nano-piezoelectric plate for pure extensional deformations are first analyzed. The performance of a nano-piezoelectric plate harvester is then investigated theoretically. Numerical results show that the effective properties and the natural frequencies of the plate are size-dependent, and the nano-piezoelectric harvester exhibits a stronger ability of converting mechanical energy into electric energy than the traditional macro- or micro-structures.