The Size-Dependent Electromechanical Coupling Response in Circular Micro-Plate due to Flexoelectricity

Flexoelectricity, the coupling of strain gradient to polarization, enhances the properties of piezoelectric response desirable for advanced MEMS dramatically even in centrosymmetric dielectrics. In this paper, the general formulations of the flexoelectric couple stress theory presented by Hadjesfandiari in orthogonal curvilinear coordinate system are derived, and are then specified for the case of cylindrical coordinates. A size-dependent flexoelectric model of circular plate is established based on the current formulations in cylindrical coordinates. The governing equations, boundary conditions and initial conditions are derived by applying Hamilton's principle. The static bending and free vibration problems of a simply supported axisymmetric circular plate are carried out to illustrate the applicability of the present model. Numerical results reveal that a homogeneous electric field between the up and down surfaces of the circular plate is induced indeed. The generated deflection, induced voltage and natural frequency show obvious size effect, but the size effect is almost diminishing as the thickness of the plate is far greater than the material length scale parameter. As the increase of the flexoelectric coefficient, the induced voltage increases evidently and the generated deflection and the natural frequency increase weakly.