Leung, Andrew Yee TakAndrew Yee TakLeungNiu, J. C.Lim, C. W.2022-04-232022-04-232009https://repository.sfu.edu.hk/handle/sfu/3068This article presents formulation of third-order non-local beam theories based on Eringen's non-local continuum theory and the Reddy and Leung higher-order beam models for bending, buckling, and vibration of nanobeams. By applying the variational principle, an asymptotic governing differential equation of infinite-order strain gradients is derived and subsequently the governing equation of motion of the nanobeams is obtained. For practical applications, the Navier solutions of the asymptotic non-local model are presented and discussed. Bending, buckling, and vibration of nanobeams with simply supported boundary conditions are investigated. Numerical examples are presented to illustrate the corresponding effects of non-local scale parameter, rotary inertia and transverse shear deformation on deflections, buckling loads, and natural frequencies of nanobeams.enjournal article10.1243/09544062JMES1501