On the nonlocal dynamics of third-order small-scale beams

Free vibrations of third-order nanobeams are investigated by exploiting an effective nonlocal methodology. Notably, the stress-driven nonlocal theory, which is a consistent tool for modeling nanostructures, is here generalized and combined with a refined shear deformation beam theory. The need for shear correction factors, which is a crucial point in nonlocal continuum mechanics, is thus bypassed by adopting a third-order nanobeam theory. The governing elastodynamic problem is mathematically described by an integro-differential formulation. An equivalent purely differential problem is derived to reduce computational burdens. Parametric analyses are carried out to investigate size dependent free vibration responses. The relevant eigenproblem is thus solved for exemplar structural schemes assessing the relative nonlocal natural frequencies and eigenfunctions. The obtained numerical outcomes can be conveniently exploited in modeling and design of ultrasmall components of smart devices.