On the vibrational analysis of small-scale flexoelectric multi-layer plates based on the modified porous EP-FG formulations

This paper aims to derive the motion equations for a small-scale flexoelectric-multilayer plate and move deep through its vibrational response to several determining variable variations. Flexoelectricity indicates the electrical polarization induction in response to the non-uniform strain gradient. As moving toward small scales, the importance and the role of this property comes more to the picture. The under-examination structure is fabricated of three layers; a mid-layer which is assumed to be composed of the porous exponential and power law-functionally graded materials, two flexoelectric face sheets, and the Vlasov foundation. The motion equations are derived mathematically based on the new EP of porous material, Hamilton’s principle, and modified couple stress theory. Utilizing the new EP power law besides evaluating the influence of the variables, length scale parameter, materials composition, geometrical characteristics, porosity, foundation parameter, and boundary conditions (B.C.s) on the dimensionless natural frequency (DNF) of such a sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes DNF and stiffness reduction in the model. Furthermore, among all considered B.C.s, simply support and clamped support refer to the lowest and the highest DNF, respectively. The content of the recent paper serves as a good source to provide a better understanding of the vibrational response of high stiffness-to-weight ratio structures to different variable variations.