Closed-form nonlinear frequency of flexoelectric nanobeams with surface and nonlocal effects under closed circuit electric field

Abstract

Nonlocal and surface effects on nonlinear vibration characteristics of a flexoelectric nanobeams under magnetic field are examined. Eringen’s nonlocal elasticity as well as surface elasticity theories are employed to describe the size-dependency of the flexoelectric nanobeam. Also, flexoelectricity is an important size-dependent phenomena for piezoelectric structures at nanoscale, related to the strain gradient-electric polarization coupling. After the derivation of governing equation via Hamilton’s principle, Galerkin method is employed to satisfy boundary conditions. Also, analytical procedures are implemented to obtain the closed-form nonlinear frequency of flexoelectric nanobeam. It is showed that magnetic field intensity, flexoelectric parameter, nonlocal parameter, elastic foundation and applied voltage on the top surface of the nanobeam have great influences on nonlinear vibration frequency.