With the assistance of molecular dynamics simulations and non-local theories of continuum mechanics, we have captured the size-dependent effects of nanostructures. Continuum models are commonly utilized to study structures' mechanical properties at macro-scales. However, these models are incapable of being employed to determine the mechanical characterization of nanomaterials. In contrast, atomistic simulations, such as molecular dynamics models, are widely accepted for studying the behavior of materials in nano-scaled systems. However, these atomic simulation techniques suffer from high computational costs. In this study, we propose that hybrid atomistic-continuum models are suitable for studying these systems' mechanical and vibrational properties. Hence, free vibrations of FCC metals nanobeams, aluminum, and silver are investigated through non-local elasticity models (Eringen differential and stress-driven models), and strain gradient models are formulated for Euler-Bernoulli and Timoshenko nanobeam. For the first time, atomistic simulation results are utilized in conjunction with the Bees algorithm optimization technique to calibrate the size parameter values for the non-classical continuum models. In this manner, the effects of size parameters on the vibration behavior of metallic nanobeams are examined. Our simulations revealed that aluminum metallic nanobeams exhibit softening and stiffening behaviors, while silver nanobeams show only softening behavior, which is one of the most significant findings of our research. Moreover, we have demonstrated that calibrated continuum models are capable of accurately predicting the mechanical vibrational behavior of nanobeams with only minimal errors.
