New Predictions of Size-Dependent Nanoscale Based on Non local Elasticity for Wave Propagation in Carbon Nanotubes

This paper has established the physics and new understanding of nonlocal nanoscale for wave propagation in carbon nanotubes (CNT) based on the nonlocal elastic stress field theory. In this paper, a new exact nonlocal CNT model based on variational principal has been developed for wave propagation. Specifically, this paper has successfully derived new higher-order governing equation of motion based on the Euler-Bernoulli model for analyzing wave propagation in CNTs. In addition to significant difference comparing to the partial nonlocal models, the dispersion relation and spectrum relation derived using this new exact nonlocal model brings an important limelight of a critical wavenumber in CNTs. Decaying of wave propagation in CNTs is observed in this exact nonlocal elastic stress model beyond the critical wavenumber while wave propagation is enhanced below this critical value. The true physics of nanoscale on wave propagation in CNTs are further illustrated by the relation of nanoscale with respect to the phase velocity. Comparison with existing nonlocal models and the new exact model are presented through examples of wave propagation in CNTs using the nonlocal elastic field equations. Qualitative comparisons with other non-nonlocal approaches including molecular dynamics simulation, strain gradients model, couple stress model and experiments justify that the stiffness enhancement conclusion as predicted by the new nonlocal stress model.