Vibration analysis of double double-walled carbon nanotubes based on Timoshenko beam theory and wave propagation approach

This paper concerned with the vibration of double walled carbon nanotubes (CNTs) as continuum model based on Timoshenko-beam theory theory. The vibration solution obtained from Timoshenko Timoshenko-beam theory provides a better presentation of vibration structure of carbon nanotubes nanotubes. The natural frequencies of double double-walled CNTs against half axial wave mode are investigatedinvestigated. The frequency decreases on decreasing the half axial wave mode mode. The shape of frequency arcs is different for various lengths lengths. It is observed that model has produc ed lowest results for C C-F and highest for C C-C. A large parametric study is performed to see the effect of half axial wave mode on frequencies of CNTs CNTs. This numerically vibration solution delivers a benchmark results for other techniques techniques. The comparison of present model is exhibited with previous studies and good agreement is found found.