| Summary: | The flexoelectric effect of materials, which is the coupling between strain gradient and electric polarization, is most noticeable for the micro/nano electromechanical systems. In the present paper, the size-dependent electromechanical properties of the bilayer piezoelectric sensor are studied and analyzed considering the strain gradient elastic and flexoelectric effects. The governing equation and the corresponding generalized mechanical boundary conditions of the bilayer cantilever sensor are derived utilizing the variational method of flexoelectric materials based on the electric Gibbs free energy. And a new piezo-flexoelectric coupling parameter is proposed and the relationship between the induced electric potential (voltage) and the rotation angles of the ends is obtained. The analytical expressions of deflection and induced electric potential are given when the bilayer piezoelectric sensor is subject to a uniform force. The numerical results show that the normalized deflection, normalized stiffness and induced electric potential are dependent on the structural size, material parameters and internal material length scale parameters. The piezoelectric effect will play a leading role in the induced electric potential when the sensor thickness is larger than a critical value. With decreasing sensor thickness, the flexoelectric and strain gradient elastic effects will dominate the induced electric potential. Moreover, an intrinsic size depending on the material properties is identified for the maximum induced electric potential. The thickness and polarization direction of the piezoelectric layer also have a great influence on the induced electric potential of the sensor systems.
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