Wave propagation in carbon nanotubes via nonlocal continuum mechanics

TLDR

The study investigates wave propagation in carbon nanotubes using two nonlocal continuum mechanics beam models and compares their applicability. The authors analyze dispersion relations, asymptotic phase velocities, and frequencies for various CNT wave numbers and diameters through theoretical analysis and numerical simulations, and estimate the nonlocal scale coefficient. The models accurately predict small‑scale effects on CNT wave propagation, with qualitative validation against published experimental reports. Reference: Mag.

Abstract

Wave propagation in carbon nanotubes (CNTs) is studied with two nonlocal continuum mechanics models: elastic Euler-Bernoulli and Timoshenko beam models [Philos. Mag. 41, 744 (1921)]. The small-scale effect on CNTs wave propagation dispersion relation is explicitly revealed for different CNTs wave numbers and diameters by theoretical analyses and numerical simulations. The asymptotic phase velocities and frequency are also derived from nonlocal continuum mechanics. The scale coefficient in nonlocal continuum mechanics is roughly estimated for CNTs from the obtained asymptotic frequency. In addition, the applicability and comparison of the two nonlocal elastic beam models to CNTs wave propagation are explored through numerical simulations. The research findings are proved effective in predicting small-scale effect on CNTs wave propagation with a qualitative validation study based on the published experimental reports in this field.