Gradient elasticity and flexural wave dispersion in carbon nanotubes

Higher-order elasticity theories have recently been used to predict the dispersion characteristics of flexural waves in carbon nanotubes (CNTs). In particular, nonlocal elasticity and gradient elasticity (with unstable strain gradients) have been employed within the framework of classical Euler-Bernoulli or improved Timoshenko beam theory to capture the dynamical behavior of CNTs. Qualitative agreement with the predictions of related molecular-dynamics (MD) simulations was observed, whereas the MD results departed significantly from those obtained with classical elasticity calculations. The present contribution aims to alert that the aforementioned higher-order models may yield questionable results for the higher wave numbers. As an alternative, gradient elasticity (with stable strain gradients), by also incorporating inertia gradients for dynamical applications, is used in combination with both Euler-Bernoulli and Timoshenko beam theories and shown to describe flexural wave dispersion in CNTs realistically for the small-to-medium range of wave numbers, i.e., the range for which MD results are available.