Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection

Abstract

Thermal post-buckling analysis of a geometrically imperfect nanoscale piezoelectric beam under closed circuit condition is performed accounting for the flexoelectricity and surface effects. The flexoelectricity is due to the coupling between electrical polarization and strain gradient. Applying Hamilton's principle, the governing equations and related boundary conditions are derived. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. Obtained results indicate that both the flexoelectricity and surface effects possess notable impact on the post-buckling behavior of the system. Only flexoelectricity yields a considerable difference between the present model and previous investigations on conventional piezoelectric nanobeams. A parametric study has been performed to examine the effects of surface elasticity, flexoelectricity, applied electric voltage, geometrical imperfection, foundation parameters and boundary conditions on post-buckling load of piezoelectric nanobeams.