On a stochastic model of nonlocal elastic beams using the generalized perturbation method

This work presents an initial investigation into uncertainty quantification and propagation in Bernoulli–Euler nonlocal elastic beams. The beams are analyzed using both classical (local) and nonlocal approaches, where the basic uncertainty sources are attributed to their geometrical parameters—i.e. the length and the nonlocal parameter. The generalized iterative stochastic perturbation technique enables theoretical development and computational determination of the basic probabilistic moments and coefficients of uncertain beam displacements. We find that the uncertainty propagation in nonlocal models of engineering beams exhibits unexpected behaviour, which is markedly different from that observed in traditional engineering mechanics. This work offers insight into what can be expected in the vibration analysis of beams using nonlocal models, as well as in broader extensions of well-established engineering theories involving frames, plates, and shells.