Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach

This paper presents the wave propagation approach for analyzing the free vibration and wave reflection in carbon nanotubes. The propagation and reflection matrices obtained by the wave propagation method are useful for the analysis of mechanical energy transmission and reflection in micro/nano devices. These matrices can also be used for obtaining the natural frequencies of carbon nanotubes. Firstly, the obtained natural frequencies by this method are compared with the results in the literature. Then, the effect of small scale on the reflected power of an incident wave upon different boundary conditions is studied in details. It was found that the reflected power of an incident wave upon a simply supported boundary is independent of the small scale, incident wave frequency, material and geometrical parameters of the carbon nanotubes while the reflected power of a wave upon clamped and free boundary conditions depends on the small scale, incident wave frequency, material and geometrical parameters.