Dramatic Effect of the Utilized Theory on Frequency Distribution Function of Carbon Nanotubes

In this study, we investigate the modal density of double-walled carbon nanotubes. Emphasis is placed on the effect of the utilized theory. Specifically, we compare the modal density obtained via classical Bernoulli–Euler theory with that obtained by employing the refined Bresse–Timoshenko theory with nonlocal and surface effects taken into account. We show that the effect of refinements is dramatic.