An efficient GDQ model for vibration analysis of a multiwall carbon nanotube on Pasternak foundation with general boundary conditions

In this article, the free transverse vibrational behaviour of a multiwall carbon nanotube (MWNT) surrounded by a Pasternak-type elastic medium has been determined using a very generalized model. The model has been made on the basis of Timoshenko elastic beam theory which allows the effects of shear deformation and rotary inertia and supports non-coaxial vibration of the adjacent layers of MWNT using interlayer van der Waals forces. The boundary conditions used in this simulation are such that not only standard and conventional kinds, but also all possible forms, of end conditions are applicable. A generalized differential quadrature method is utilized to solve the governing equations with assorted aspect ratios, various boundary conditions, and different foundation stiffnesses. This study shows that the resonant frequencies of MWNTs are strongly dependent on the stiffness of the elastic medium, aspect ratios, and number of walls in carbon nanotubes and, for short nanotubes, the boundary stiffness plays a significant role on the natural frequencies.