4.7 Article

An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects

Journal

COMPOSITES PART B-ENGINEERING
Volume 52, Issue -, Pages 199-206

Publisher

ELSEVIER SCI LTD
DOI: 10.1016/j.compositesb.2013.04.023

Keywords

Nano-structures; Surface properties; Vibration; Analytical modeling

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Nonlinear free vibration of simply supported FG nanoscale beams with considering surface effects (surface elasticity, tension and density) and balance condition between the FG nanobeam bulk and its surfaces is investigated in this paper. The non-classical beam model is developed within the framework of Euler-Bernoulli beam theory including the von Karman geometric nonlinearity. The component of the bulk stress, sigma(zz), is assumed to vary cubically through the nanobeam thickness and satisfies the balance conditions between the FG nanobeam bulk and its surfaces. Accordingly, surface density is introduced into the governing equation of the nonlinear free vibration of FG nanobeams. The multiple scales method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanbeams. Several comparison studies are carried out to demonstrate the effect of considering the balance conditions on free nonlinear vibration of FG nanobeams. Lastly, the influences of the FG nanobeam length, volume fraction index, amplitude ratio, mode number and thickness ratio on the normalized nonlinear natural frequencies of the FG nanobeams are discussed in detail. (C) 2013 Elsevier Ltd. All rights reserved.

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