Free vibration of the bi-dimensional functionally grated (2D-FG) nanobeams

Abstract

In this paper, the free vibration of the bi-dimensional functionally grated (2D-FG) size dependent nanobeams was investigated by finite element method. The material properties of 2D-FG nanobeam are assumed to vary in both axial and thickness directions by power gradation laws. The size-dependent 2D-FG nanobeam is studied on the basic of nonlocal continuum model. Based on the Euler-Bernoulli beam theory, a finite nanobeam element is derived and employed in vibration analysis of the beam. A parametric study has been carried out to show the effect of material distribution, nonlocal effect on the natural frequencies of the beams.