Natural frequency of size-dependent microplates with piezoelectric layers

The main purpose of the present paper is to study free vibration of nonclassical micro plates with piezoelectric layers. To this end, the plate is modeled according to Kirchhoff's plate theory. Piezoelectric layers are modeled according to linear piezoelectricity theory and due to the small thickness, the electric field is assumed to be constant in these layers. The strain energy of the system is obtained using modified couple stress theory (MCST) and the governing equation of motion is derived using Hamilton's principle. The finite element model is used to solve the obtained equations and effects of piezoelectric layers and material length parameter scale on the natural frequency of the system are studied.