Stress-driven approach for stochastic analysis of noisy nonlocal beam

Several structures, such as micro/nano-devices, long-fiber reinforced composites, beam with external patches, exhibit a mechanical behavior that cannot be described by classical local continuum model. For these structural elements, since the long-range interactions cannot be neglected, it is needed the introduction of an enriched mechanical model that takes into account these nonlocal effects. For this reason, during the last decades, several scientific efforts have been dedicated to the formulation of various nonlocal mechanical models. Among these formulations, the stress-driven approach has been recently developed. In addition to overcome some limitations and paradoxes of the classic integral non-locality, such recent integral model allows to obtain some closed-form solutions. Specifically, for bending problems, the stress-driven formulation provides the analytical solutions in terms of transverse displacement for several static cases. In this work the stress-driven approach is used to perform the stochastic dynamic analysis of nonlocal beams. The natural frequencies and the eigenfunctions of nonlocal Euler-Bernoulli beam are evaluated, and the Power Spectral Density function of the displacement response due to a Gaussian white noise input is provided for different values of the nonlocal parameters. Such kind of problem is of interest for the applications of nano-and micro-beams as actuators and sensors where stochastic analysis is needed to reproduce the real load cases and the size effect causes the nonlocal mechanical behavior.