Abstract: “In this study, vibration of effect of nanoparticle on an Euler-Bernoulli nano-beam is investigated using nonlocal elasticity beam theory. Equation of motion of nanobeam is obtained using Hamilton’s principle. The dimensionless equations are solved for the various boundary conditions. Approximate solutions of the equations are obtained by using the method of multiple scales a perturbation technique. The first terms of the perturbation series lead to the linear problem. Exact solutions are given natural frequencies for the linear problem. The effects of the different nonlocal parameters () and mass ratios () as well as effects of different boundary conditions on the vibrations are determined.”

Keywords: vibration, nanobeam, nanoparticle, perturbation method, nonlocal elasticity