Assessment of first and third order shear deformation beam theories for the buckling and vibration analysis of nanobeams incorporating surface stress effects

•Incorporating surface effect can significantly alter the estimated buckling and vibration results of single crystalline nanobeams.•Besides the beam geometric parameters, elements of metal and crystallographic directions will also significantly influence the results.•When nanobeams are thin and with significant surface effects, the generic 3rd order beam theory gives more accurate results due to the inclusion of the non-vanishing shear stress effect at the interface between the surface layer and the bulk of the beams.•If nanobeam thickness is more than 80nm and with less significant surface effects, there is negligible difference of the buckling and vibration results obtained either using the 1st order, the Reddy 3rd order or the generic 3rd order beam theories. A novel approach for the vibration and buckling analysis of nanobeams with surface stress effects is presented in this paper. The material model is derived in which the bulk core of a beam is assumed to be a single crystalline material and have certain crystallographic directions. The beams are assumed to be covered by atomic layers with the same crystallographic directions on the top and bottom surfaces. A generic third order shear deformable beam theory is employed to derive the total energy functional of the beams. Minimizing the total potential energy functional by applying the p-Ritz method, the eigenvalue equations for the buckling and vibration of nanobeams with surface stress effects are obtained. The buckling and vibration behaviours of the beams considering the surface stress effects are discussed in detail and are compared with the results obtained from the first order beam theory and the Reddy's third order beam theory. It is found that in certain cases, both the first order and the Reddy's third order beam theories may not be able to capture the surface effect accurately on the vibration and buckling behaviours of the nanobeams. The effects of surface stresses on the buckling and vibration behaviours for nanobeams made of Ni single crystals obtained by the generic third order beam theory showed opposite trends to the ones obtained by the first order or the Reddy's third beam theory. [Display omitted]