On non-linear vibrations of flexoelectric nanobeams

In this article, non-linear vibration problem of flexoelectric nanobeams with surface and thermal effects is investigated. Flexolectricity in piezoelectric nanobeams can be interpreted as the strain gradient-electrical polarization coupling. There are two flexoelectric mechanisms which are direct and converse flexoelectricity. An electric voltage is applied to the top surface of the nanobeam which introduces a closed-circuit electric field condition. Employing He's variational method, the nonlinear governing equation of flexolectric nanobeam is solved and nonlinear frequencies are obtained. The flexielectricity effect is less important for large scale beams, therefore it has a great influence on vibration behavior of piezoelectric nanobeams. Also, the effects of several parameters including temperature change, elastic foundation, surface coefficients and nanobeam thickness on nonlinear frequency are investigated.