Size-scale effects on bending behaviour of nanobeam on an elastic substrate medium

This paper presents a new nonlocal beam-substrate medium model for the static bending analysis of micro- and nano-sized Euler-Bernoulli beam systems resting on an elastic substrate medium. The modified couple stress theory (MCST) represents the small-scale effect ( nonlocal effect) inherent in microand nanoscale structures. The Winkler-Pasternak foundation model is used to model the characteristics of the underlying substrate medium, while the surface continuum model of Gurtin and Murdoch is employed to account for the size-dependent effect (surface-energy effect). The governing differential equation and its associated boundary conditions for the proposed beam-substrate medium model are derived based on the principle of virtual displacement. These equations are employed to assess the bending behavior of the nanobeam system on the elastic substrate medium. The analytical results are discussed through a numerical simulation, and this reveals that the small-scale effect, as well as size-dependent and substrate-structure interaction effects, lead to stiffness enhancement in the system.