Surface Effects on Free Vibration Analysis of Nanobeams Using Nonlocal Elasticity: A Comparison Between Euler-Bernoulli and Timoshenko

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress through the nanobeam thickness. The governing equations are obtained and solved for Silicon and Aluminum nanobeams with three different boundary conditions, i.e. Simply-Simply, Clamped-Simply and Clamped-Clamped. The results show that the influence of the surface effects on the natural frequencies of the Aluminum nanobeams follows the order CC < CS < SS while this is not the case for Silicon nanobeams. On the other hand, the influence of the nonlocal parameter is opposite and follows the order SS < CS < CC. In addition, it is seen that considering rotary inertia and shear deformation has more effect on the surface effects than the nonlocal parameter.