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.