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Advances in Materials Science and Engineering
Volume 2015, Article ID 318539, 7 pages
Research Article

Nonlinear Vibrational Analysis of Nanobeams Embedded in an Elastic Medium including Surface Stress Effects

1Department of Environmental Sciences, School of Agriculture and Environmental Sciences, University of South Africa, P.O. Box 1710, Florida, South Africa
2Young Researchers and Elite Club, Electronic Branch, Islamic Azad University, Tehran, Iran
3Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Received 26 July 2015; Revised 16 November 2015; Accepted 22 November 2015

Academic Editor: Santiago Garcia-Granda

Copyright © 2015 S. Azizi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Due to size-dependent behavior of nanostructures, the classical continuum models are not applicable for the analyses at this submicron size. Surface stress effect is one of the most important matters which make the nanoscale structures have different properties compared to the conventional structures due to high surface to volume ratio. In the present study, nonlinear free vibrational characteristics of embedded nanobeams are investigated including surface stress effects. To this end, a thin surface layer is assumed on the upper and lower surfaces of the cross section to separate the surface and bulk of nanobeams with their own different material properties. Based on harmonic balance method, closed-form analytical solution is conducted for nonlinear vibrations to obtain natural frequencies of embedded nanobeams with and without considerations of surface elasticity and residual surface tension effects corresponding to the various values of nondimensional amplitude, elastic foundation modulus, and geometrical variables of the system. Selected numerical results are given to indicate the influence of each one in detail.