Size-dependent free vibration analysis of infinite nanotubes using elasticity theory

Exact elasticity theory is employed to study the (two-dimensional) free vibration of nanoscale cylindrical tubes in the presence of free surface energy.Use is made of the Gurtin-Murdoch surface elasticity model to incorporate the surface stress terms into the pertinent boundary conditions.Some numerical examples are provided to depict the influence of the surface energy, and particularly the inner radius size of the nanocylinder, on the natural frequencies of the system.The results indicate a stronger influence of surface effects for both smaller values of the outer to inner radius ratio and higher modes of vibration.Yaser Mirzaei is the corresponding author.