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) elasticity Bernoulli-Euler kinematics. The developed methodology is applicable a wide variety nano-engineered materials, such as carbon nanotubes, modern small-scale beam-like devi...