Vibrational Analysis of Double-walled Carbon Nanotubes Based on the Nonlocal Donnell Shell Theory via a New Numerical Approach

Abstract– This article describes an investigation into the free vibration of double-walled carbon nanotubes (DWCNTs) using a nonlocal elastic shell model. Eringen’s nonlocal elasticity is implemented to incorporate the scale effect into the Donnell shell model. Also, the van der Waals interaction between the inner and outer nanotubes is taken into account. A new numerical solution method from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature (GDQ) method is developed to solve the problem. DWCNTs with arbitrary layerwise boundary conditions are considered in this paper. It is shown that applying the local Donnell shell model leads to overestimated results and one must recourse to the nonlocal version to reduce the relative error. Also, this work reveals that in contrast to the beam model, the present nonlocal elastic shell model is capable of predicting some new noncoaxial inter-tube resonances in studying the vibrational response of DWCNTs.