Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler-Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between PG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the PG nanobeam thickness. The nonlinear governing equation includes the von Kiribati geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of PG nanobeams is investigated. (C) 2014 Elsevier Inc. All rights reserved.