Analysis of Mechanical Properties of Flexoelectric Nano-plates Based on Nonlocal Strain Gradient Theory

At present, nano-plates with flexoelectric effect have become a research hotspot because they are not affected by material symmetry, so the range of material choices is significantly expanded compared with traditional piezoelectric materials. In this study, considering the flexoelectric effect and utilizing the nonlocal strain gradient theory (NSGT), a novel model is introduced for analyzing transversely isotropic rectangular nano-plates under a distributed load. This new model takes into account nonlocal effect, size effect, and flexoelectricity. By applying the Hamilton principle, the governing equations are derived for two different circuits. In order to verify the validity of the new model, we compare it with the results of the finite element method (FEM) and give its first eight mode shapes. At the same time, the theoretical model is numerically solved, and based on the numerical results, the mechanical properties of the flexoelectric nano-plate are analyzed and discussed. The theoretical and simulation results of this paper provide a reliable theoretical support for the design of devices based on flexoelectric nano-plates.