Parviz Malekzadeh

In the present work, at first, the drawbacks of the continuum mechanics (CM) based method in predicting the vibrational and wave dispersion characteristics of carbon nanotubes (CNTs) are illustrated and discussed. For this purpose, the response of the Euler-Bernoulli and Timoshenko beam theories together with the differential form of the Eringen’s nonlocal elasticity theory under different boundary conditions are examined. The same problems are simulated via molecular dynamics (MD) approach. By considering the results of MD simulation as the benchmark solutions, it is shown that the optimum value of the length scale parameter of the nonlocal elasticity theory of Eringen depends on the nanotube boundary conditions, aspect ratio and vibrational mode number of the CNTs. To overcome these drawbacks, a kernel with unique length scale variable is introduced by combing different Gaussian kernels and specifying two related new scale variables. These newly defined scale parameters resolve former problem in shifting between different scales. Accordingly, an improved nonlocal constitutive relation is suggested. It is shown that the proposed model can accurately predict the vibrational and flexural vibrational dispersion relation (FVDR) characteristics of CNTs even when using Euler-Bernoulli theory (EBT).