A theoretical approach for flexural behavior of FG vibrating micro-plates with piezoelectric layers considering a hybrid length scale parameter

In the current study, the mechanical performance of functionally graded oscillating micro-plates bonded with piezoelectric layers is examined using the modified couple stress theory. The modified couple stress theory contains a length scale parameter that considers the size-effects of micro-plates. The various modified shear deformation theories are employed to represent the displacement field of micro-plate, such as exponential, parabolic, hyperbolic, trigonometric, and fifth-order shear deformation theories. The properties of FG micro-plate, such as Young’s modulus, density, and length scale parameter, are assumed to vary smoothly and across the micro-plate thickness based on the Power-law model. The governing equations of motion are obtained by Hamilton's principle and solved by a theoretical approach under various boundary conditions. The accuracy of the proposed model is validated based on a comparison of the results with the accepted studies. Computational analysis is carried out to clarify the impacts of mechanical and geometrical variables on the natural frequencies of micro-plates.