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

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.