Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams

A modified continuum model of the nanoscale beams is presented by incorporating surface elasticity in this paper. The classical beam theory is adopted to model the bulk, while the bulk stresses along the surfaces of the bulk substrate are required to satisfy the surface balance equations of the continuum surface elasticity. On the basis of this modified beam theory the governing equation of the nanobeam is derived where the effect of the geometry nonlinearity is also considered. The Galerkin method is used to give a reduced-order model of the problem. Beams made from two materials: aluminum and silicon are chosen as examples. The numerical results show that the mechanical buckling and free vibration phenomena of nanobeams are size-dependence. The effects of the surface energies on the critical axial force of buckling, post-buckling and linear free vibration frequency are discussed. Finally, the amplitude frequency response is given numerically through the incremental harmonic balanced method.