Size-dependent electromechanical responses of a bilayer piezoelectric microbeam

On the basis of the couple stress piezoelectric theory including flexoelectric effects, a size-dependent model of a bilayer microbeam consisting of a piezoelectric material layer and an elastic layer has been established. The governing equations along with the boundary conditions of the microbeam model have been obtained from variation principle. The microbeam bending problems have been solved to analyse the electromechanical coupling responses to the applied concentrated force and voltage. Numerical results show that whether under the concentrated force or the voltage, the influence of flexoelectric effects on the equivalent piezoelectric response is larger than that of rotation gradient elastic effects when the size of the microbeam is much larger than the material length scale parameters. However, with the continuous decrease of the beam characteristic size scale, rotation gradient elastic effects have a stronger impact on the electromechanical responses than flexoelectric effects, which leads to a rapid decrease of the equivalent piezoelectric responses. The result also shows that the contribution of flexoelectric effects on the equivalent piezoelectric response increases when the beam size diminishes, which leads to a significant surge of the electromechanical responses compared to the model under the classical piezoelectric theory.