Wave characteristics of carbon nanotubes

The research in the manuscript studies the wave characteristics in carbon nanotubes (CNTs) via beam theories. First, the material properties used in the beam models for the analysis of CNTs are proposed from the discrete atomic nature of CNTs. Secondly, the comparison of wave solution in a single walled carbon nanotube (SWNT) by Euler–Bernoulli beam model and Timoshenko beam model is conducted. The applicability of the two beam models is discussed from the numerical simulations. In addition, the difference of the two beam models on the terahertz frequency range is presented to show the significance of applying an appropriate continuum model in studying the wave propagation in CNTs. Thirdly, Timoshenko beam model is employed to study the wave propagation in a double walled carbon nanotube (DWNT) via a simple single beam theory by assuming co-axial motion of the two tubes, and a double beam theory accounting for van der Waals. The size effect of the DWNT on the wave solution by different beam theories is discussed as well. The feasibility of applying the simple single beam theory and the double beam theory is discussed through numerical simulations. It is hoped that the research in the manuscript may present a benchmark in the study of wave propagations in carbon nanotubes.