Surface stress and non-local elasticity effects on the free vibration behavior of nanobeams

Abstract

This paper presents the effects of surface stress and non-local elasticity on the free vibration of nanobeams with various boundary conditions. Analytical solutions for natural frequencies and corresponding mode shapes of the nanobeams are derived and compared numerically by using the finite element method. Identical results between the two solution methods are obtained. The obtained results indicate that the surface stress and non-local elasticity affect directly the free vibration behavior of the nanobeams. The effect of surface stress is to increase the stiffness of the nanobeams. Therefore, the natural frequencies of the nanobeams for all boundary conditions increase in comparison with that of the classical Euler beam. Moreover, the surface stress affects significantly only for the lower modes of vibration. In the case of nonlocal elasticity effect, it reduces the natural frequencies of the nanobeams, especially for the higher modes of vibration. For the nanobeams subjecting to both effects, the results show that the natural frequencies are in between one of the nanobeams with surface stress and the one with non-local elasticity. This gives a practical implication that not only the surface stress but also non-local elasticity affects directly on the vibration behavior of the nanobeams. However, the surface stres\\s affects only the lower modes of vibration and therefore the result