Exploring the source of non-locality in the Euler–Bernoulli and Timoshenko beam models

In the last decade there has been significant research activity in the use of Eringen’s nonlocal models to reformulate the equations of beams and plates. All of the previous works used a length scale parameter to study its effect on bending, buckling, and vibration characteristics, without identifying what the length scale parameter means. An attempt is made herein, for the first time, to relate the length scale parameter(s) to physical parameters. The Eringen’s non-local Euler–Bernoulli and Timoshenko beam models are identified as continuum limits of a discrete system comprising of harmonic oscillators. The correspondence between the coefficients of the discrete and the continuum models is used to determine the source of the non-locality in the context of Eringen’s non-local beams.