Investigating nonlinear vibration of closed circuit flexoelectric nanobeams with surface effects via Hamiltonian method

This paper is motivated by the lack a study on nonlinear vibration behavior of flexoelectric nanobeams. Nonlinear vibration analysis of a nanoscale piezoelectric beam resting on nonlinear elastic foundation 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. Close form of nonlinear frequency is obtained implementing Hamiltonian method. Obtained results indicate that both the flexoelectricity and surface effects possess notable impact on the nonlinear frequencies 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, foundation parameters, geometrical parameters and boundary conditions on nonlinear frequencies of piezoelectric nanobeams.