Nonlinear free vibration of nanowires including size effects

Considering the transverse shear deformation, geometric nonlinearity and the surface effects as well as the non-local effects, the nonlinear free vibration of nanowires is studied in this Letter. On the basis of the Timoshenko beam theory and Hamilton´s principle, the nonlinear dynamics equations and corresponding boundary conditions of nanowires are derived. Then, the Galerkin method and the incremental harmonic balance method are adopted to solve the nonlinear equations. In numerical examples, the effects of the transverse shear deformation, geometric nonlinearity, surface effects as well as the non-local effects on the nonlinear amplitude´frequency response of nanowires are discussed.