Quasi-3D free and forced vibrations of poroelastic microplates in the framework of modified couple stress theory

In this study, a comprehensive study on the vibration behaviour of functionally graded thick microplates with material imperfections is presented for free and forced vibrations within a quasi-3D model and the modified couple stress (MCS) theory. Axial, transverse, rotation, and stretching motions are considered for modelling the thick microplate in the framework of the modified power-law scheme and quasi-3D and MCS theories. The microplate deformation is assumed to be infinitesimal and is modelled using the linear strain–displacement relationships. Using a virtual work method, the governing motion equations are derived. For fourfold coupled (axial-transverse-rotation-stretching) characteristics, the partial differential equations components are discretised via trigonometric expressions and the corresponding natural frequencies and time histories (time-dependent deflections) are determined numerically. The methodology and model are initially validated through a comparative analysis between the natural frequencies of the macrolevel simplified structure and those obtained using finite element software. Additionally, the simulation is compared, for validation purposes, with other simplified versions from the literature. Once model's validity is confirmed, an investigation into the quasi-3D free and forced vibrations of the structure is conducted for the new model. The results demonstrate the considerable effect of thickness stretching and material imperfection on the vibration characteristics of the poroelastic thick microplates.