Free vibration and static deflection of a micro-plate with piezoelectric layers using modified couple stress theory

In this syudy, a size-dependent modeling of micro plate with piezoelectric layers based on classical plate theory using modified couple stress theory is developed in this paper. Introducing only one material length scale parameter in modified couple stress theory to take into account the size effect of the system is one of the main advantage of this theory over other nonclassical continuum mechanics theories. Also, this theory is able to predict and interpret the size-dependent static and dynamic behavior of micro-scale structures with more accuracy and precision in comparison to classical continuum mechanics theory. The piezoelectric layers are modeled according to linear piezoelectricity theory and due to small thickness, the electric field is assumed to be constant over the layers. The equation of motion and its corresponding boundary conditions are derived using Hamilton principle. The equation of motion is solved numerically using finite element method and the effect of material length scale parameter and piezoelectric layers on free vibration and static deflection of micro-plate are investigated.