  In this article, eigenfrequencies of nano-beams under axial loads are
assessed by making recourse to the well-posed stress-driven nonlocal model
(SDM) and strain-driven two-phase local/nonlocal formulation (NstrainG) of
elasticity and Bernoulli-Euler kinematics. The developed nonlocal methodology
is applicable to a wide variety of nano-engineered materials, such as carbon
nanotubes, and modern small-scale beam-like devices of nanotechnological
interest. Eigenfrequencies calculated using SDM, are compared with NstrainG and
other pertinent results in literature obtained by other nonlocal strategies.
Influence of nonlocal thermoelastic effects and initial axial force (tension
and compression) on dynamic responses are analyzed and discussed. Model
hardening size effects from stress-driven approach is compared to model
softening size effects from strain-driven two-phase local/nonlocal approach for
increasing nonlocal parameters.
