Quasi-3D plate theory for size-dependent static and free vibration analysis of FG microplate with porosities based on a modified couple stress theory

This work presents a static and vibration analysis of a porous functionally graded (FG) microplate using a simplified quasi-3D plate formulation and a modified couple stress theory that requires only one material length scale parameter. The theory contains only five unknowns, incorporating undetermined integral variables in accordance with the first-order shear deformation theory (FSDT). The model satisfies the zero traction boundary conditions on the upper and lower surfaces of the microplate. The governing equations are obtained via Hamilton's principle and subsequently solved using Navier-type closed-form solutions. The proposed theoretical model is validated by comparing it with existing models in the literature to demonstrate its efficacy. The influence of the length scale parameter, the power law index, shear and normal deformation effects, porosity factors, and plate thickness on the responses of microplates is examined through the presentation of numerical examples. The findings show that taking size effects into account increases the stiffness of the microplate, which in turn reduces deflections and raises natural frequencies. Conversely, the normal and shear deformation influences have the opposite impact.