Vibrational response of a sandwich microplate considering the impact of flexoelectricity and based on a novel porous-FGM formulation

Flexoelectricity indicates a unique characteristic of insulators and dielectric materials that results in electrical polarization induction in response to the non-uniform strain gradient. The impact of this property is bolder on the microscale and nanoscale rather than the macroscale. This article is conducted to derive the governing equations of motion for a flexoelectric-multilayer structure and evaluate its vibrational behavior in response to various variable variations. The model includes a functionally graded (FG) porous core which is confined between two flexoelectricity-based face sheets at both sides and a Vlasov type of foundation. To gain the governing equations, the new type of power law for porous material beside Hamilton's principle (HP) and modified couple stress theory (MCST) is implemented. Capturing the effects of length scale parameter, different materials, aspect and thickness ratios, porosity index, foundation parameter and boundary conditions (B.C.s) on the normalized natural frequency (NNF) of such a multilayer model based on the novel FG porous material formulation serve as the main novelty of this article. According to the results, it is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered B.C.s, simply support (SSSS) and clamped support (CCCC) refer to the lowest and the highest NNF respectively. The content of the recent article 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.