On stochastic free vibrations of Eringen’s two-phase elastic nanobeams

This study develops a probabilistic framework for analyzing free vibration of nanobeams using the generalized differential quadrature method (GDQM) as the numerical solver. The approach’s configuration (asymmetrical and bi-orthogonal) requires a procedure distinct from existing works to couple with the second-order stochastic perturbation method (SOSPM). Specifically, a particular form of undamped vibration based on a primary displacement field (Bernoulli-Euler) and harmonic assumption is investigated in this work. Furthermore, integrating small-scale effects of Eringen’s two-phase (local/nonlocal) elasticity theory, a consistent mathematical size-dependent theory, with probabilistic uncertainties provide an opportunity to predict the nonlocal factor, which is an essential parameter in the approach. Ultimately, the reliability of the second-order stochastic perturbation method is evaluated.