چكيده به لاتين
The aim of this Treatise is to study The Longitudinal natural frequency of nanobeams considering surface effects.it should be said that, in nanoscale neglecting the surface effects is not appropriate decision, because ratio of surface to volume is significant. In this Treatise, these effects for longitudinal free vibration in nanoscale have been studied. equation of surface stress obtained from Gibbs free Energy relations and equation of motions have been derived from Hamilton principle based on Simple theory, Rayleigh's theory and the theory of Bishop's. Since parameters of surface effects appear in boundary condition equations, it causes boundary conditions heterogeneity and it is difficult to solve the problem. These effects enter the equation as external work to homogenize the equations of boundary conditions. In the following, derived equations of motion have been solved by Modal analysis method. nanobeam motional function and natural frequency have been presented with or without crack. Finally, effects of parameters such as length, diameter and material of nanobeam, mode number, crack parameter and crack location in three first natural frequencies with clamped-clamped boundary condition have been studied.
Key word:
Longitudinal Free vibration – Cracked nanobeam – Surface effects – Modal analysis – Natural frequency
