Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects

This article is concerned with the thermo-mechanical vibration behavior of flexoelectric nanoplates under uniform and linear temperature distributions. Flexoelectric nanoplates have higher natural frequencies than conventional piezoelectric nanoplates, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric nanoplates for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions, which are solved applying the Galerkin-based solution. A comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameters, surface elasticity, temperature rise, plate thickness, and various boundary conditions on the vibration frequencies of thermally affected flexoelectric nanoplate.