Nonlinear oscillation of nanowires, based on the Timoshenko beam theory, are investigated. The analytical solution of the nanowire structure using the Galerkin technique together with the variational iteration method is developed. A coupled nonlinear differential equation is obtained utilizing the Galerkin technique. Subsequently, the frequency-amplitude relationships are found for the nonlinear vibration of the nanowires using the variational iteration method. The main objective of this work is to obtain the frequency-amplitude relationships of the nanowires and also to investigate the effects of different parameters, such as the surface effect, transverse shear deformation and the aspect ratio, on their dynamic behaviors. Furthermore, the influence of varying amplitude on the nonlinear oscillations of the nanowires is analyzed.
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